(1)...c€€€€€€€the radio waves become polarised as a result of adjusting the aerial....

(a) The diagram below represents a progressive wave travelling from left to right on astretched string.

(i) Calculate the wavelength of the wave.

answer ____________________ m

(1)

1

(ii) The frequency of the wave is 22 Hz. Calculate the speed of the wave.

answer____________________m s–1

(2)

(iii) State the phase difference between points X and Y on the string, giving anappropriate unit.

answer ____________________

(2)

(b) Describe how the displacement of point Y on the string varies in the next half-period.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(Total 7 marks)

(a) State the characteristic features of

(i) longitudinal waves,

______________________________________________________________

______________________________________________________________

2

of 51St Bede's Catholic Comprehensive School and Byron College

(ii) transverse waves.

______________________________________________________________

______________________________________________________________

(3)

(b) Daylight passes horizontally through a fixed polarising filter P. An observer views the lightemerging through a second polarising filter Q, which may be rotated in a vertical planeabout point X as shown in Figure 1.

Figure 1

Describe what the observer would see as Q is rotated slowly through 360°.

You may be awarded marks for the quality of written communication provided inyour answer.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(Total 5 marks)


displacement

The graph shows, at a particular instant, the variation of the displacement of the particles in atransverse progressive water wave, of wavelength 4 cm, travelling from left to right. Which one ofthe following statements is not true?

A The distance PS = 3 cm.

B The particle velocity at Q is a maximum.

C The particle at S is moving downwards

D Particles at P and R are in phase.

(Total 1 mark)

3

A wave of frequency 5 Hz travels at 8 km s–1 through a medium. What is the phase difference, inradians, between two points 2 km apart?

A 0

B

C π

D

(Total 1 mark)

4

A source emits light of wavelength 600 nm as a train of waves lasting 0.01 µs. How manycomplete waves are sent out?speed of light = 3 × 108 m s−1

A 5 × 106

B 18 × 107

C 5 × 109

D 5 × 1022

(Total 1 mark)

5


Stationary waves are set up on a length of rope fixed at both ends. Which one of the followingstatements is true?

A Between adjacent nodes, particles of the rope vibrate in phase with each other.

B The mid point of the rope is always stationary.

C Nodes need not necessarily be present at each end of the rope.

D Particles of the rope at adjacent antinodes always move in the same direction.

(Total 1 mark)

6

Two points on a progressive wave differ in phase by . The distance between them is 0.5 m,and the frequency of the oscillation is 10 Hz. What is the minimum speed of the wave?

A 0.2 m s−1

C 10 m s−1

C 20 m s−1

D 40 m s−1

(Total 1 mark)

7

Which line, A to D, in the table gives a correct difference between a progressive wave and astationary wave?

progressive wave stationary wave

Aall the particles vibrate some of the particles do not

vibrate

Bnone of the particles vibratewith the same amplitude

all the particles vibrate withthe same amplitude

Call the particles vibrate inphase with each other

none of the particles vibrate inphase with each other

Dsome of the particles do notvibrate

all the particles vibrate inphase with each other

(Total 1 mark)

8


Which line, A to D, in the table shows correct relationships for the respective wavelengths, λL, λS,

and frequencies, fL, fS, of light waves and sound waves?

wavelengths frequencies

A λL << λS fL >> fS

B λL << λS fL << fS

C λL >> λS fL >> fS

D λL >> λS fL << fS

(Total 1 mark)

9

Which one of the following properties of light waves do polarising sunglasses depend on for theiraction?

Light waves may

A interfere constructively.

B interfere destructively.

C be polarised when reflected from a surface.

D be polarised by the lens in the eye.

(Total 1 mark)

10

The speed of sound in water is 1500 m s−1. For a sound wave in water having frequency 2500

Hz, what is the minimum distance between two points at which the vibrations are rad out ofphase?

A 0.05 m

B 0.10 m

C 0.15 m

D 0.20 m

(Total 1 mark)

11


The diagram shows a snapshot of a wave on a rope travelling from left to right.

At the instant shown, point P is at maximum displacement and point Q is at zero displacement.Which one of the following lines, A to D, in the table correctly describes the motion of P and Q inthe next half-cycle?

P Q

A falls then rises rises

B falls then rises rises then falls

C falls falls

D falls rises then falls

(Total 1 mark)

12

An aerial system consists of a horizontal copper wire of length 38 m supported between twomasts, as shown in the figure below. The wire transmits electromagnetic waves when analternating potential is applied to it at one end.

(a) The wavelength of the radiation transmitted from the wire is twice the length of the copperwire. Calculate the frequency of the transmitted radiation.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(1)

13


(b) The ends of the copper wire are fixed to masts of height 12.0 m. The masts are held in avertical position by cables, labelled P and Q, as shown in the figure above.

(i) P has a length of 14.0 m and the tension in it is 110 N. Calculate the tension in thecopper wire.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(ii) The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper wire.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(iii) Discuss whether the wire is in danger of breaking if it is stretched further due tomovement of the top of the masts in strong winds.

breaking stress of copper = 3.0 × 108 Pa

______________________________________________________________

______________________________________________________________

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______________________________________________________________

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(7)

(Total 8 marks)


A stationary wave is formed by two identical waves of frequency 300 Hz travelling in oppositedirections along the same line. If the distance between adjacent nodes is 0.60 m, what is thespeed of each wave?

A 180 m s−1

B 250 m s−1+

C 360 m s−1

D 500 m s−1

(Total 1 mark)

14

By approximately how many times is the wavelength of audible sound waves greater than thewavelength of light waves?

A 102

B 106

C 1010

D 1014

(Total 1 mark)

15


In testing a particular type of guitar string, a string is stretched and vibrated for a long period oftime using a mechanical vibrator as shown in Figure 1. The right-hand end of the string is fixed.A stationary wave is produced on the string; the string vibrates in two loops.

Figure 1

(a) State the conditions that are necessary for a stationary wave to form on the string.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

16

(b) Explain how you know that the wave on the string is transverse.

___________________________________________________________________

(1)

(c) Compare the amplitude and phase of the oscillations of points A and B on the string.

Amplitude __________________________________________________________

Phase _____________________________________________________________

(2)

(d) The length of the string is 1.2 m and the speed of the transverse wave on the string is 6.2m s–1.

Calculate the vibration frequency of the vibrator in Hz.

Vibration frequency ____________________Hz

(3)


(e) (i) The frequency of the vibrator is tripled.Sketch the new shape of the stationary wave on Figure 2.

Figure 2

(ii) Show on your diagram three points P, Q and R that oscillate in phase.

(2)

(Total 11 marks)

A microwave transmitter is used to direct microwaves of wavelength 30 mm along a line XY. Ametal plate is positioned at right angles to XY with its mid-point on the line, as shown.

When a detector is moved gradually along XY, its reading alternates between maxima andminima. Which one of the following statements is not correct?

A The distance between two minima could be 15 mm.

B The distance between two maxima could be 30 mm.

C The distance between a minimum and a maximum could be 30 mm.

D The distance between a minimum and a maximum could be 37.5 mm.

(Total 1 mark)

17


The sound quality of a portable radio is improved by adjusting the orientation of the aerial.Which statement is a correct explanation of this improvement?

A The radio waves from the transmitter are polarised.

B The radio waves from the transmitter are unpolarised.

C The radio waves become polarised as a result of adjusting the aerial.

D The radio waves become unpolarised as a result of adjusting the aerial.

(Total 1 mark)

18

Figure 1 represents a stationary wave formed on a steel string fixed at P and Q when it isplucked at its centre.

Figure 1

(a) Explain why a stationary wave is formed on the string.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

19

(b) (i) The stationary wave in Figure 1 has a frequency of 150 Hz. The string PQ has alength of 1.2 m.Calculate the wave speed of the waves forming the stationary wave.

Answer ____________________ m s–1

(2)


(ii) On Figure 2, draw the stationary wave that would be formed on the string at thesame tension if it was made to vibrate at a frequency of 450 Hz.

Figure 2

(2)

(Total 7 marks)

Complete the first column in the table to show which of the waves listed are transverse andwhich are longitudinal.Complete the second column to show which waves can be polarised.

type of wave transverse orlongitudinal

can be polarised(answer yes or no)

light

microwaves

ultrasound

(Total 3 marks)

20

The figure below shows two ways in which a wave can travel along a slinky spring.

(a) State and explain which wave is longitudinal.

___________________________________________________________________

___________________________________________________________________

(2)

21

(b) On the figure above,

(i) clearly indicate and label the wavelength of wave B

(1)


(ii) use arrows to show the direction in which the points P and Q are about to move aseach wave moves to the right.

(2)

(c) Electromagnetic waves are similar in nature to wave A.

Explain why it is important to correctly align the aerial of a TV in order to receive thestrongest signal.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(Total 7 marks)

Figure 1 shows a side view of a string on a guitar. The string cannot move at either of the twobridges when it is vibrating. When vibrating in its fundamental mode the frequency of the soundproduced is 108 Hz.

(a) (i) On Figure 1, sketch the stationary wave produced when the string is vibrating in itsfundamental mode.

Figure 1

(1)

22

(ii) Calculate the wavelength of the fundamental mode of vibration.

answer = ____________________ m

(2)


(iii) Calculate the speed of a progressive wave on this string.

answer = ____________________ m s–1

(2)

(b) While tuning the guitar, the guitarist produces an overtone that has a node 0.16 m frombridge A.

(i) On Figure 2, sketch the stationary wave produced and label all nodes that arepresent.

Figure 2

(2)

(ii) Calculate the frequency of the overtone.

answer = ____________________ Hz

(1)

(c) The guitarist needs to raise the fundamental frequency of vibration of this string.State one way in which this can be achieved.

___________________________________________________________________

___________________________________________________________________

(1)

(Total 9 marks)


(a) (i) A piano string has a tension of 681 N. It vibrates with a fundamental frequency (firstharmonic) of 92.5 Hz and has a mass per unit length of 1.87 × 10–2 kg m–1.Calculate the length of the string.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

length of string ______________________ m

(3)

23

(ii) The figure below shows a string stretched between fixed ends.Draw onto the figure the first overtone (second harmonic) mode of vibration.

(1)

(iii) State how you could make a string on a stringed instrument vibrate in this mode ofvibration.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(2)


(b) Describe how you would investigate the variation of the fundamental frequency (firstharmonic) of a string with its length.State which variable(s) you would need to control and how you would do so.You may wish to assist your account by drawing a diagram.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

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(4)

(Total 10 marks)


The figure below shows a continuous progressive wave on a rope. There is a knot in the rope.

(a) Define the amplitude of a wave.

___________________________________________________________________

___________________________________________________________________

(2)

24

(b) The wave travels to the right.Describe how the vertical displacement of the knot varies over the next complete cycle.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

(c) A continuous wave of the same amplitude and frequency moves along the rope from theright and passes through the first wave. The knot becomes motionless.Explain how this could happen.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

(Total 8 marks)


When a note is played on a violin, the sound it produces consists of the fundamental and manyovertones.

Figure 1 shows the shape of the string for a stationary wave that corresponds to one of theseovertones. The positions of maximum and zero displacement for one overtone are shown. PointsA and B are fixed. Points X, Y and Z are points on the string.

Figure 1

(a) (i) Describe the motion of point X.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(2)

25

(ii) State the phase relationship between

X and Y _______________________________________________________

X and Z _______________________________________________________

(2)

(b) The frequency of this overtone is 780 Hz.

(i) Show that the speed of a progressive wave on this string is about 125 ms–1.

(2)

(ii) Calculate the time taken for the string at point Z to move from maximum displacementback to zero displacement.

answer = ____________________ s

(3)


(c) The violinist presses on the string at C to shorten the part of the string that vibrates.Figure 2 shows the string between C and B vibrating in its fundamental mode. The lengthof the whole string is 320 mm and the distance between C and B is 240 mm.

Figure 2

(i) State the name given to the point on the wave midway between C and B.

______________________________________________________________

(1)

(ii) Calculate the wavelength of this stationary wave.

answer = ____________________ m

(2)

(iii) Calculate the frequency of this fundamental mode. The speed of the progressivewave remains at 125 ms–1.

answer = ____________________Hz

(1)

(Total 13 marks)


(a) State two differences between stationary waves and progressive waves.

first difference _______________________________________________________

___________________________________________________________________

___________________________________________________________________

second difference ____________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

26

(b) A violin string has a length of 327 mm and produces a note of frequency 440 Hz.Calculate the frequency of the note produced when the same string is shortened or“stopped” to a length of 219 mm and the tension remains constant.

frequency ______________________ Hz

(2)

(Total 4 marks)

Describe a laboratory experiment to investigate how the fundamental frequency of a stretchedstring depends on the tension in the string.The stretched string has a mass per unit length of 1.5 × 10–3 kg m–1.

Your detailed method should include:• a labelled diagram of the experiment arrangement• suitable estimates of any quantities involved in the experiment• how you would use the data to demonstrate the relationship between fundamentalfrequency and tension.

The quality of your written communication will be assessed in your answer.

(Total 6 marks)

27

(a) Musical concert pitch has a frequency of 440 Hz.A correctly tuned A-string on a guitar has a first harmonic (fundamental frequency) twooctaves below concert pitch.

Determine the first harmonic of the correctly tuned A-string.

frequency____________________ Hz

(1)

28


(b) Describe how a note of frequency 440 Hz can be produced using the correctly tunedA-string of a guitar.

___________________________________________________________________

___________________________________________________________________

(1)

(c) Describe the effect heard when notes of frequency 440 Hz and 430 Hz of similar amplitudeare sounded together.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(Total 4 marks)


Earthquakes produce transverse and longitudinal seismic waves that travel through rock. Thediagram below shows the displacement of the particles of rock at a given instant, for differentpositions along a transverse wave.

(a) State the phase difference between

(i) points A and B on the wave ______________________________________

(ii) points A and C on the wave ______________________________________

(2)

(b) Describe the motion of the rock particle at point B during the passage of the next completecycle.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

29

(c) A scientist detects a seismic wave that is polarised. State and explain what the scientistcan deduce from this information.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)


(d) The frequency of the seismic wave is measured to be 6.0 Hz.

(i) Define the frequency of a progressive wave.

______________________________________________________________

______________________________________________________________

(1)

(ii) Calculate the wavelength of the wave if its speed is 4.5 × 103 m s–1.

wavelength ____________________ m

(2)

(Total 9 marks)

Ultrasound waves are used to produce images of a fetus inside a womb.

(a) Explain what is meant by the frequency of a wave.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(1)

30

(b) Ultrasound is a longitudinal wave. Describe the nature of a longitudinal wave.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(c) In order to produce an image with sufficient detail, the wavelength of the ultrasound mustbe 0.50 mm. The speed of the ultrasound in body tissue is 1540 m s–1. Calculate thefrequency of the ultrasound at this wavelength.Give your answer to an appropriate number of significant figures.

frequency ____________________ Hz

(2)


(d) A continuous ultrasound wave of constant frequency is reflected from a solid surface andreturns in the direction it came from.

Assuming there is no significant loss in amplitude upon reflection, describe and explain theeffect the waves have on the particles in the medium between the transmitter and the solidsurface.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

(Total 8 marks)

(a) Explain what is meant by a progressive wave.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

31


(b) Figure 1 shows the variation with time of the displacement of one point in a progressivewave.

Figure 1

Figure 2 shows the variation of displacement of the same wave with distance.

Figure 2


Use Figures 1 and 2 to determine

(i) the amplitude of the wave

amplitude = ____________________ mm

(1)

(ii) the wavelength of the wave

wavelength = ____________________ m

(1)

(iii) the frequency of the wave

frequency = ____________________ Hz

(1)

(iv) the speed of the wave

speed = ____________________ m s−1

(1)

(c) Which of the following statements apply?Place a tick (✔) in the right-hand column for each correct statement.

✔ if correct

sound waves are transverse

sound waves are longitudinal

sound waves can interfere

sound waves can bepolarised

(1)


(d) In an investigation, a single loudspeaker is positioned behind a wall with a narrow gap asshown in Figure 3.

A microphone attached to an oscilloscope enables changes in the amplitude of the soundto be determined for different positions of the microphone.

Figure 3

The amplitude of sound is recorded as the microphone position is moved along the line ABa large distance from the gap.


The result of the measurements is shown in Figure 4.

Figure 4

The signal generator is adjusted so that sound waves of the same amplitude but of a higherfrequency are emitted by the loudspeaker. The investigation using the apparatus shown inFigure 3 is then repeated.Explain the effect this has on Figure 4.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(3)

(Total 10 marks)


A stationary wave is formed on a stretched string. Discuss the formation of this wave.Your answer should include:

• an explanation of how the stationary wave is formed• a description of the features of the stationary wave• a description of the processes that produce these features.

The quality of your written communication will be assessed in your answer.

(Total 6 marks)

32

The frequency of the first harmonic of a standing wave on a wire is f. The length of the wire andtension in the wire are both doubled.

What is the frequency of the first harmonic as a result?

A

B f

C

D 2f

(Total 1 mark)

33

Musicians can use tuning forks to tune their instruments.A tuning fork produces a specific frequency when it vibrates.

Figure 1 shows a tuning fork vibrating in air at a single instant in time.The circles represent the positions of air particles in the sound wave.

Figure 1

34

(a) The tuning fork emits a wave that has a frequency of 0.51 kHz.

(i) State the meaning of the term frequency of a wave.

______________________________________________________________

(1)


(ii) Air particles vibrate in different phases in the direction in which the wave is travelling.

Calculate the minimum separation of particles that vibrate 180° out of phase.

speed of sound in air = 340 m s–1

minimum separation ____________________ m

(3)

(b) A student sets a tuning fork of lower frequency vibrating at the same time as the 0.51 kHztuning fork in part (a).

The student detects the resultant sound wave with a microphone. The variation with time ofthe voltage generated by the microphone is shown in Figure 2.

Figure 2

(i) Explain why the two tuning forks are not coherent sources of sound waves.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(2)


(ii) Explain why the resultant sound has a minimum amplitude at 50 ms.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(3)

(iii) Calculate the frequency of the tuning fork that emits the lower frequency.

frequency ____________________ Hz

(3)

(c) A signal generator connected to a loudspeaker produces a sinusoidal sound wave with afrequency of 440 Hz.

The variation in air pressure with time for this sound is shown in Figure 3.

Figure 3


A violin string has a fundamental frequency (first harmonic) of 440 Hz.

Figure 4 shows the variation in air pressure with time for the sound created by the violinstring.

Figure 4

(i) The two sounds have the same pitch but sound different.

What term describes the difference between the sounds heard?Tick (✔) the correct answer.

Frequency modulation

Octaves

Path difference

Quality

(1)

(ii) The complex sound in Figure 4 can be electronically synthesised.

Describe the process of electronically synthesising this sound.

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

______________________________________________________________

(3)

(Total 16 marks)


(a) Define the amplitude of a wave.

___________________________________________________________________

___________________________________________________________________

(1)

35

(b) (i) Other than electromagnetic radiation, give one example of a wave that is transverse.

______________________________________________________________

(1)

(ii) State one difference between a transverse wave and a longitudinal wave.

______________________________________________________________

______________________________________________________________

(1)

(c) The figure below shows two identical polarising filters, A and B, and an unpolarised lightsource. The arrows indicate the plane in which the electric field of the wave oscillates.

(i) If polarised light is reaching the observer, draw the direction of the transmission axison filter B in the figure below.

(1)


(ii) The polarising filter B is rotated clockwise through 360º about line XY from theposition shown in the figure above. On the axes below, sketch how the light intensityreaching the observer varies as this is done.

(2)

(d) State one application, other than in education, of a polarising filter and give a reason for itsuse.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

(2)

(Total 8 marks)


Mark schemes

(a) (i) 0.4(0) m (1)

(ii) speed ( = frequency × wavelength) = 22 × 0.4(0) ecf (1)= 8.8 (m s–1) (1)

(ii) 90 or 450 (1) ° or degrees (1)or 0.5π or 2.5π or 5π/2 (1) rad(ians)or r or r (1) no R, Rad, etc

5

1

(b) displacement of Y will be a positive (or ‘up’) maximum at 1/4of a period (or cycle) (0.0114 s) (1)

returns to original position (at 0.5 of a period or cycle) (owtte) (1)2

[7]

(a) (i) particle vibration (or disturbance or oscillation) (1)same as (or parallel to) direction of propagation(or energy transfer) (1)

(ii) (particle vibration)perpendicular to direction of propagation (or energy transfer) (1)

3

(b) variation in intensity between max and min (or light and dark) (1)two maxima (or two minima) in 360° rotation (1)

2QWC 1

[5]

2

D

[1]3

B

[1]4

A

[1]5

A

[1]6

D

[1]7

A

[1]8

A

[1]9


C

[1]10

B

[1]11

D

[1]12

(a) λ(=2 × 38) = 76(m)

MHz (1)

1

13

(b) (i) angle between cable and horizontal = (1)

T= 110 cos59° = 57N • (56.7N) (1)

(allow C.E. for value of angle)

(ii) cross-sectional area (= P(2.0 × 10–3)2)

=1.3 × 10–5(m2) (1)

(1.26 × 10–5(m2))

stress (1)

= 4.4 × 106Pa (1)

(4.38 × 106Pa)(use of 56.7 and 1.26 gives 4.5 × 106 Pa)(allow C.E. for values of T and area)

(iii) breaking stress is 65 × stresscopper is ductilecopper wire could extend much more before breakingbecause of plastic deformationextension to breaking point unlikely

any three (1)(1)(1)7

[8]

C

[1]14

B

[1]15


(a) reflection implied/2 waves in opposite directions/fixed end (not ends) (1)

similar amplitude/little energy loss at wall (1)

frequency constant or same frequency/wavelength or correct wavelengthcondition specified (1)

3

16

(b) displacement perpendicular to rest/average/mean position of string

or string displacement perpendicular to energy propagationdirection owtte (1)

1

(c) A larger than B (1)

A 180° (or π rad) out of phase with B (owtte) (1)2

(d) λ = 1.2 (1)

c = f λ; allow e.c.f from wrong λ (1)

f = 6.2/1.2 = 5.2 Hz (1)3

(e) (i) diagram correct (6 loops) (1)

(ii) Q and R correctly in phase with P; must be a position wheremovement occurs (1)

2

[11]

C

[1]17

A

[1]18

(a) (progressive waves travel from centre) to ends and reflect (1)

two (progressive) waves travel in opposite directions along the string (1)

waves have the same frequency (or wavelength) (1)

waves have the same (or similar) amplitude (1)

superposition (accept ‘interference’) (1)max 3

19

(b) (i) wavelength (= 2 × PQ = 2 × 1.20 m) = 2.4 m (1)

speed (= wavelength × frequency = 2.4 × 150) = 360 m s–1 (1)

(answer only gets both marks)


(ii) diagram to show three ‘loops’ (1) and of equal length andgood shape (1) (or loop of one third length (1))

4

[7]

transverse yes

B1

transverse yes

B1

longitudinal no

B1

[3]

20

(a) (wave) B

(the parts of the) spring oscillate / move back and forth in direction of / parallelto wave travelORmention of compressions and rarefactions

Second mark can only be scored if first mark is scored2

21

(b) (i) (double ended arrow / line / brackets) from between two points in phase 1

(ii) wave A: arrow vertically upwards

wave B: arrow horizontally to the left 2

(c) (transmitted radio waves are often) polarised

aerial (rods) must be aligned in the same plane (of polarisation / electric field) ofthe wave

2

[7]

(a) (i) one ‘loop’ (accept single line only, accept single dashed line)

+ nodes at each bridge (± length of arrowhead)

+ antinode at centre (1)1

22


(ii) λ0 = 2L or λ = 0.64 × 2 (1)

= 1.3 (m) (1) (1.28)2

(iii) (c = f λ) = 108 × (a)(ii) (1)

= 138 to 140(.4) (m s–1) (1) ecf from (a) (ii)2

(b) (i) four antinodes (1) (single or double line)

first node on 0.16 m (within width of arrowhead)

+ middle node between the decimal point and the centre of the‘m’ in ‘0.64 m’

+ middle 3 nodes labelled ‘N’, ‘n’ or ‘node’ (1)2

(ii) (4 f0 =) 430 (Hz) (1) (432)

or use of f = gives 430 to 440 Hz correct answer only, no ecf

1

(c) decrease the length/increase tension/tighten string (1)1

[9]

(a) (i) rearrangement of f = to give l = C1

correct subs l = or 92.5 =

C1

1.0(3) (m) condone sf

A13

23

(ii) 2 loops roughly equal

B11

(iii) (lightly) stop (in centre) B1

pluck or bow B1 2


(b) keeps tension or mass per unit length constant

B1

way of measuring frequency or producing vibration of known f

B1

way of measuring length (at resonance)

B1

use of suitable graph (f vs 1/l or l vs 1/f) to display results

B1

marks may be awarded for information seen on diagram4

[10]

(a) the maximum displacement (of the wave or medium)

from the equilibrium position

accept ‘rest position’, ‘undisturbed position’, ‘mean position’2

24

(b) (vertically) downwards (¼ cycle to maximum negative displacement)

then upwards (¼ cycle to equilibrium position and ¼ cycle to maximumpositive displacement)

down (¼ cycle) to equilibrium position/zero displacement and correctreference to either maximum positive or negative displacement or correctreference to fractions of the cycle

candidate who correctly describes the motion of a knot 180 degrees out ofphase with the one shown can gain maximum two marks(ie knot initially moving upwards)

3

(c) max 3 from

stationary wave formed

by superposition or interference (of two progressive waves)

knot is at a node

waves (always) cancel where the knot is

allow ‘standing wave’3

[8]


(a) (i) oscillates / vibrates

(allow goes up and down / side to side / etc, repeatedly, continuously, etc)

about equilibrium position / perpendicularly to central line 2

25

(ii) X and Y: antiphase / 180 (degrees out of phase) / п (radians out of phase)

X and Z: in phase / zero (degrees) / 2п (radians) 2

(b) (i) v = fλ

= 780 x 0.32 / 2 or 780 x 0.16 OR 780 x 320 / 2 or 780 x 160

THIS IS AN INDEPENDENT MARK

= 124.8 (m s–1) correct 4 sig fig answer must be seen2

(ii) ¼ cycle

T = 1 / 780 OR = 1.28 × 10–3

0.25 × 1.28 × 10–3

= 3.2 × 10–4 (s)

Allow correct alternative approach using distance of 0.04m

travelled by progressive wave in ¼ cycle divided by speed.

0.04 /125 = 3.2 × 10–4 (s) 3

(c) (i) antinode 1

(ii) 2 x 0.240

= 0.48 m ‘480m’ gets 1 mark out of 22

(iii) (f = v/λ = 124.8 or 125 / 0.48 ) = 260 (Hz) ecf from cii 1

[13]


(a) max 2 from

in progressive waves, all points have the same amplitude (in turn),in stationary waves, they do not

B1

in stationary waves, points between nodes are in phase, in progressivewaves, all points within one wavelength are out of phase witheach other

B1

in stationary waves, there is no energy transfer along the wave,in progressive waves, there is

B1

stationary waves have nodes and antinodes but progressive waves do not

B1

where there are single relevant statements but no clear comparisonbetween stationary and compressive waves, award 1 mark fortwo such statements

2

26

(b) f α 1/l orƒ= or fl = const

C1

657/660 (Hz)

A12

[4]


The marking scheme for this question includes an overall assessment for the quality of writtencommunication (QWC). There are no discrete marks for the assessment of QWC butthe candidate’s QWC in this answer will be one of the criteria used to assign a leveland award the marks for this question.

Descriptor – an answer will be expected to meet most of the criteria in the level descriptor.Level 3 – good-claims supported by an appropriate range of evidence-good use of information or ideas about physics, going beyond those given in the question-argument well structured with minimal repetition or irrelevant points-accurate and clear expression of ideas with only minor errors of grammar, punctuation andspellingLevel 2 – modest-claims partly supported by evidence,-good use of information or ideas about physics given in the question but limited beyond this theargument shows some attempt at structure-the ideas are expressed with reasonable clarity but with a few errors of grammar, punctuationand spellingLevel 1 – limited-valid points but not clearly linked to an argument structure-limited use of information about physics-unstructured-errors in spelling, punctuation and grammar or lack of fluencyLevel 0-incorrect, inappropriate or no response

27

Level 3Response will give a sensible diagram, suggestion of length of string and sensible range detailsof range of tension, the procedure to obtain data and the analysis of the data. The response mayinclude a calculation of f for the chosen apparatus.

Level 2All bullet points will be addressed but may lack essential detail. The response will include asensible diagram and procedure but the procedure may be poorly explained. It should includehow the data is analysed to demonstrate the relationship.

Level 1Attempt will contain some relevant detail of a sensible experiment. The diagram may be poorlydrawn. The range for the tension may be given but not be sensible. Their procedure and analysismay be only superficially described.

Level 0Response will contain no relevant information about an appropriate experiment.


Points that may be included

• Labelled diagram including string , weights, pulley, metre rule,

• method using signal generator (calibrated) and magnets to causeoscillation of the string

• method using tuning forks

• Length 1-2 m

• e.g Weights up to 12 N in 2 N increments (range of at least 6)

• Frequencies different by detectable amount on sig gen / use ofrange of tuning forks

• Calculation to show approx f value for selected T and l

• Method of changing T

• How frequency is determined for each T

• Graph of f against √T[6]

(a) 110 Hz

B11

(b) (Use finger on the fret so that) a ¼ length of the string is used to sound the note orhold string down on 24th fret

B11

28

(c) Mention or description of beats or description of rising and falling amplitude / louderand quieter

Regular rising and falling of loudness owtte

B1

B1

Beat frequency 10(.0Hz) Allow beat frequency = 430 - 4202

[4]

(a) (i) π / 2 (radians) or 90 (degrees)

No path differencesPenalise contradictionsNo fractions of a cycle

1

29

(ii) 3π / 2 (rad) or 270 (degrees)

No path differencesPenalise contradictionsNo fractions of a cycle

1


(b) (oscillation or motion) perpendicular to direction of wave (travel / velocity / energytransfer) (oscillates from equilibrium to maximum positive displacement, back to equilibrium,then to max negative displacement) and back to equilibrium / starting position / restposition

do not allow ‘up and down’ for first markallow ‘up and down’, or ‘down then up’, ‘side to side’, ‘rise and fall’in place of oscillatesAllow ‘rest position’, ‘starting position’ ,‘middle’, ‘centre line’

ref to nodes / antinodes not allowed for 2 nd mark2

(c) (the wave is) transverse OR not longitudinal

accept it is an S wave or secondary wave

only transverse can be polarised OR longitudinal waves cannot be polarisedOR oscillations are in one plane

2

(d) (i) number of waves / complete cycles / wavelengths (passing a point / produced)per second

or ‘unit time’allow: (number of) oscillations / vibrations / cycles per secondallow f=1 / T only if T is correctly defineddo not allow references to f=c / λ

1

(ii) ( v = f / λ λ = v / f = ) 4.5 × 103 / 6.0 = 750 (m)

correct answer only gets 2 marks2

[9]

(a) number of (complete) waves (passing a point) in 1 secondORnumber of waves / time (for the waves to pass a point)OR(complete number of) oscillations \ vibrations per secondOR1 / T with T defined as time for 1 (complete) oscillation ✓

Allow: cycles

Allow: unit time1

30


(b) For two marks:oscillation of particles \ medium \ material etc, but not oscillation of wave is parallel to\ in same direction asthe direction wave (travels) ✓ ✓

For one mark:particles \ material \ medium move(s) \ disturbance \ displacementparallel to \ in same direction asthe direction wave travelsOR(oscillations) parallel to direction of wave travel ✓

the one mark answer with: mention of compressions and rarefactions OR (longitudinal waves) cannot be polarised

gets two marks✓

AllowVibration

Allow direction of energy transfer \ wave propagation2

(c) ( f = 1540 / 0.50 × 10−3 )= 3 100 000 (Hz) ✓ (3 080 000)2sf ✓

2

(d) no more than two points from either list (max 3):Description • mention of nodes and antinodes • particles not moving at a node • maximum displacement at antinode • particles either side of node in antiphase / between two nodes in phase • variation of amplitude between nodes

Explanation • a stationary wave (forms) • two waves are of equal frequency or wavelength (and amplitude in the same medium) • reflected and transmitted waves \ waves travelling in opposite directions, pass through each other • superpose / interference occurs • constructive interference at antinodes • destructive interference at nodes

✓ ✓ ✓Allow ‘standing wave’

3

[8]


(a) A wave transfers energy from one point to another ✔without transferring material / (causing permanent displacement of the medium) ✔ owtte

2

31

(b) (i) 0.6 (mm) or 0.60 (mm) ✔1

(ii) 0.080 (m) ✔Allow 1 sig fig

1

(iii) f = 1/T = 1/0.044 = 23 (Hz) ✔ (22.7 Hz)1

(iv) v = f λ = 22.7 × 0.080 = 1.8 (m s-1) ✔ (1.82 m s-1)

allow CE v = (biii) × (bii) but working must be shown

1 sig fig not acceptable1

(c)

soundwaves aretransverse

soundwaves arelongitudinal

soundwaves caninterfere

soundwaves can

bepolarised

√ √ 1

(d) the wavelength would be smallersmaller spread in main peak or more peaks (between A and B)the central peak is higher (owtte)as the energy is concentrated over a smaller area (owtte)

reference to (sin θmin = λ/d)✔ ✔ ✔ any 3 lines max 3

Note that the marks here are for use of knowledge rather thanperforming calculations.

No bod if writing does not make increase or decrease clearlydistinct.

Marking should be lenient.3

[10]


The student’s writing should be legible and the spelling, punctuation and grammar shouldbe sufficiently accurate for the meaning to be clear.

The student’s answer will be assessed holistically. The answer will be assigned to one ofthree levels according to the following criteria.

Answers may cover some of the following points:• (1) a wave and its reflection / waves travelling in opposite directions

meet / interact / overlap / cross / pass through etc

point (1) must be stated together i.e it should not be necessary tosearch the whole script to find the two parts namely the directions ofthe waves and their meeting

• (2) same wavelength (or frequency)• (3) node − point of minimum or no disturbance

points (3) may come from a diagram but only if the node is written infull and the y-axis is labelled amplitude or displacement

• (4) antinode − is a point of maximum amplitudepoint (4) may come from a diagram but only if the antinode iswritten in full and the y-axis is labelled amplitude or displacement

• (5) node - two waves (always) cancel / destructive interference / 180° phasedifference / in antiphase [out of phase is not enough] (of the two waves at thenode) [not peak meets trough]

• (6) antinode − reinforcement / constructive interference occurs /(displacements) in phase

• (7) mention of superposition [not superimpose] of the two waves• (8) energy is not transferred (along in a standing wave).

if any point made appears to be contradicted elsewhere the point islost − no bod’s

High Level (Good to excellent): 5 or 6 marksThe information conveyed by the answer is clearly organised, logical and coherent, usingappropriate specialist vocabulary correctly. The form and style of writing is appropriate toanswer the question.

6 marks: points (1) AND (2) with 4 other points which must include point (4) or the passagemust indicate that the wave is oscillating at an antinode

5 marks: points (1) AND (2) with any three other points

although point (1) may not be given as a mark the script can besearched to see if its meaning has been conveyed as a wholebefore restricting the mark and not allowing 5 or 6 marks

Intermediate Level (Modest to adequate): 3 or 4 marksThe information conveyed by the answer may be less well organised and not fully coherent.There is less use of specialist vocabulary, or specialist vocabulary may be used incorrectly.The form and style of writing is less appropriate.

4 marks: (1) OR (2) AND any three other points3 marks: any three points

Low Level (Poor to limited): 1 or 2 marksThe information conveyed by the answer is poorly organised and may not be relevant or

32


coherent. There is little correct use of specialist vocabulary.The form and style of writing may be only partly appropriate.

2 marks: any two points1 marks: any point or a reference is made to both nodes and antinodes

[6]

A

[1]33

(a) (i) Number of complete waves passing a point in one second / number of completewaves produced by a source in one second / number of complete vibrations(oscillations) per second / number of compressions passing a fixed point persecond

1

34

(ii) 180° phase difference corresponds to ½ λUse of v = fλ with correct powers of 100.33 (m)

3

(b) (i) Do not have the same frequencydo not have a constant phase difference

2

(ii) Waves meet antiphaseUndergo superpositionResulting in destructive interference

3

(iii) T = 100 ms

Use of T = 1 / f or beat frequency (∆f) = 10 Hz500 (Hz) (allow 510 –their beat frequency)

3

(c) (i) Only box ticked: Quality1

(ii) Add regular alternating voltages togetherWith appropriate amplitudesWhere frequencies of voltages match the harmonics of sound / where frequenciesare multiples of 440 Hz

Allow 2 for sampling sound (at twice max frequency ) B1

Convert to binary ( and replay through D to A converter). B13

[16]


(a) maximum displacement from equilibrium/meanposition/mid-point/etc (1)

1

(b) (i) any one from:

surface of water/water waves/in ripple tank (1)

rope (1)

slinky clearly qualified as transverse (1)

secondary (‘s’) waves (1)max 1

35

(ii) transverse wave: oscillation (of medium) is perpendicular towave travel

or transverse can be polarised

or all longitudinal require a medium (1)1

(c) (i) vertical line on B ± 5° (1)1

(ii)

max 0, 180, 360 + min 90, 270 (1)

and line reaches same minimum and maximum every timeand reasonable shape (1)

2


(d) appropriate use (1)

reason for Polaroid filter being used (1)

eg

Polaroid glasses/sunglasses/ to reduce glare windscreens

camera reduce glare/enhance image

(in a) microscope to identify minerals/rocks

polarimeter to analyse chemicals/concentration or type of sugar

stress analysis reveals areas of high/low stress/ other relevant detail

LCD displays very low power/other relevant detail

3D glasses enhance viewing experience, etc2

[8]


(1)...c€€€€€€€the radio waves become polarised as a result of adjusting the aerial....

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