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1.0 WAVES1.1 UNDERSTANDING WAVES

WAVESCause by vibrations or oscillations.Transport energy without permanently displacing the medium.Can either be a Mechanical waves which require a medium to travel eg. Sound wave or Electromagnetic waves which do not require a medium to travel.There are two types of waves:

Longitudinal Waves:The vibration of the particles of the medium is along the same direction as the motion of the wave.eg. Waves on springs and sound waves.Transverse Waves:The vibration of the particles of the medium is perpendicular (up and down ) to the motion of the wave.eg. Water waves, rope waves and waves on springs.

Direction of oscillations

Direction of oscillationsDirection of waveIn longitudinal waves, particles oscillate along line of wave direction Direction of wave

Oscillations are at right angles to direction of motion

Push

CCCC

RRRCrestRight

PullDirection of wave motion of a slinky.Direction ofvibration

Trough

C- Compression, R- RarefactionsLeftDirection of wave motion of a slinky

Activity 1.1 a : Transverse and Longitudinal Waves.

1. If the vibrations of a wave are at right angles to the direction of the wave, it is called a

wave. An example of this type of wave is .

2. If the vibrations of a wave are along the direction of the wave, it is called a

wave. An example of this type of wave is

3. Given a string tied to a pole, how would you shake the string in order to produce :(a) a transverse wave?

(b) a longitudinal wave?

4. State the difference between a transverse wave and a longitudinal wave.

WAVEFRONTSAn imaginary line representing all the points of a wave that are in the same phase.For example a wavefront can be drawn by joining all the crests of a wave.The direction of wave travel is always perpendicular to the wavefront.Figures below show how circular wavefronts and plane wavefronts are produced.

Plane WavefrontsCircular Wavefronts

Activity 1.1 (b)

1. Waves can be drawn on paper using lines to join adjacent points of the waves which are

.These lines are known asof the wave.If

the lines are straight, then they are known asbut if the lines are

circular, then they are known as. 2. The direction of propagation of a wave is always to the

of the waves.

3. Draw the direction of propagation of wave for each of the following wavefronts.

a)b)

DESCRIBING WAVES MOTION

DownwardsOscillations ofA loaded spring and a pendulumUpwards X Y Z

Graph below shows the displacement of the above rope along its length at a certain instant of time.

CrestCrestDisplacement/m

+ A

Amplitude A

Distance/m

Amplitude -A

-B

Trough

TermSymbolExplanations

Amplitude aThe maximum displacement of the oscillator from its equilibrium position.

Wavelength Distance between any two successive wave crests, troughs or points which are in phase.

Crests and troughs-High points and low points that characterize transverse waves only.

DISPLACEMENT-TIME GRAPH

Displacement/m

T

Q +a

PQa

RMean

RRPositionTime/s

Positive displacement T

P

Negativedisplacement -a

TermSymbolUnitExplanation

Period TSecond(s)The time required for one complete cycle.

Frequency fHertz(Hz)The number of complete cycles per second

f = and T =

AmplitudAmplitudDisplacementDISPLACEMENT DISTANCE GRAPH

Distance

In one period (T), a crest will have moved a distance of one wavelength ().Therefore the speed of the wave, v is given by:V= (but )

Therefore Wave velocityV=

Worked example 1:

0.3mThe above figure shows waves moving on a slinky with frequency 3 Hz and a wavelength of 0.3m.What is the wave speed?

Given frequency of wave, f = 3 HzWavelength of wave, = 0.3 mThe wave speed v = f = (3)(0.3) = 0.9 ms-1

Actvity 1 .1(c) :

1. The wavelength of a wave is the between two successive or . The unit for wavelength is .

2. The frequency is the number of oscillations made in second

The unit for frequency is .

3. The velocity of a wave is equal to multiplied by.

4. The time taken for a vibrating system to make a complete oscillation is known as.

5. The number of complete oscillations made by a vibrating system is known as.

6. The distance travelled by awave in one second is known as .

7.If the period of an oscillating system is 0.2 s and its wavelength is 60 cm, what is the velocity of the wave formed by this oscillating system ?

Given T = and =

Therefore f = =

By using the formula v = f

Therefore v =

8. Sketch a displacement-distance graph for a wave, showing two complete oscillations.On your graph, mark:(a) The wavelength of the wave,(b) The amplitude of the wave

DAMPING AND RESONNANCE

Energy transfer in vibration system

X Potential energy is maximum.

Y Kinetic energy is maximum

Z Potential energy is maximum

X Z Y

A Simple Pendulum

Displacement x/cm

a1

a2a3

a4

Time/s

a1>a2> a3> a4

Damping occurs if a vibrating system gradually loses its energy in overcoming resistance to its motion and will eventually stop vibrating.Decreasing amplitude is due to energy loss.

Example: An empty swing that is swinging will eventually come to a stop after sometime if it is not pushed.

RESONANCE

Natural frequency:The frequency that an object tends to oscillate at when disturbed by an external force.Forced Oscillation:An oscillation caused by external force acting on the system.The tendency of an object to absorb more energy when the frequency of the oscillations matches the objects natural frequency of vibration therefore causing its amplitude to grow larger and larger rapidly

Resonance: A phenomenon that happens when a vibration system is forced to vibrate with its natural frequency.

Resonance:Can be observed using a Bartons Pendulum.The Driving Pendulum forces six pendulums of different lengths to vibrate.

Bartons Pendulum : Each of the six pendulum has its natural frequency.The pendulum that vibrates with the largest amplitude is said to be in resonance with the driving pendulum.

l2l1

l3

l4x

l5

Driving penduluml6

Pendulum with various length

Example: If an Opera sings at the same frequency as the natural frequency of a glass, the glass tends to absorb more and more energy and eventually will break.

TRUE STORY

On the morning of November 7, 1940, the four month old Tacoma Narrows Bridge began to oscillate dangerously up and down. A reporter drove out on the bridge with his cocker spaniel in the car. The bridge was heaving so violently that he had to abandon his car and crawl back to safety on his hands and knees.At about 11:00 the bridge tore itself apart and collapsed. It had been designed for winds of 120 mph and yet a wind of only 42 mph caused it to collapse. How could this happen? No one knows exactly why. However, the experts do agree that somehow the wind caused the bridge to resonate. It was a shocking calamity although the only loss of life was the cocker spaniel.

Activity 1.1 (d):

1. The natural frequency of a pendulum depends on the of the pendulum and is independent of .

2. Explain what happens to a vibrating system after it is allowed to vibrate over a long period of time.

3. Resonance occurs when the applied of the driving vibration is equal to the

of the vibrating system.

4. If two strings on the same guitar are tuned to exactly the same frequency and one of them is plucked, a) What will happen to the other string?

b) What is the effect stated in (a) called?

5.Sketched the displacement time graph for a vibrating system that is experiencing:a) Very slightly damping. Displacement

Time

b) Very heavy damping.

Displacement

Time

ASSESSMENTS.OBJECTIVE QUESTIONS.

1.Which of the graph shown below represents a wave of an amplitude 2.0 cm and frequency 20 Hz?

A B

C D2.The diagram shows a wave traveling in the sea.

P R

Q S T

Which points are exactly one wavelength apart ?A P and R B Q and SC Q and T D S and T

3.A wave transfersA molecules. B energyC matter D force4.Water waves are being generated in a ripple tank at a rate of 5 Hz .This means that in one second the number of wavefronts passing through a fixed point is:A 0.2 B 2.5 C 5.0 D 10.0 E 12.0

5.Which of the following is an example of longitudinal waves ?A Waves in a ripple tank.B Light waves in water.C A vibrating guitar string.D Sound waves produced by a string.6.In air, what is the wavelength of sound of frequency 2500 Hz ?The speed of sound in air is 330ms-1.A 0.004 m B 0.003 m

C 0.132 m D 7.58 m

E 6.7 m

7.A source vibrates at a frequency of 20 Hz and produces waves of wavelength 0.02m.What is the speed with which the waves travel out from the source?A 0.001 ms-1. B 0.02 ms-1C 0.40 ms-1 D 20 ms-1 8. The incidents listed below involve resonance except : A A glass will break when a Soprano sings infront of it. B Certain parts of a bus vibrated as the bus moves. C An egg breaks as it falls down on a floor.

Displacement9.

0Time

What are the effects on frequency and energy of the wave shown in the above displacement time graph as the time increases.FrequencyEnergy

Aincreaseno change

Bincreasedecrease

Cno changeincrease

Dno changedecrease

10. Which of the following produces longitudinal waves? A B C D

STRUCTURED QUESTION.

Q1. A wave source of frequency 1000 Hz emits waves length 0.10 m. How long does it take for the waves to travel 2500 m ?

(a) Explain the meaning of the expression the frequency is 1000 Hz ?

Q2. Figure below shows a student setting up waves on a long elastic cord. The students hand makes one Complete up-and-down movement in 0.40 s, and in each up-and-down movement the hand moves Through a height of 0.30 m. The wavelength of the waves on the string is 0.80 m.

0.3 m For this wave, determine :(a) The amplitude

(b) The frequency

(c) The speed.

Q3(a) Figure below shows the graph of the variation of the displacement of a wave with distance along the wave at a particular time.

Displacement (m) State values for:

Distance/m0.6 (i) the amplitude of the wave.

10

-0.6

(ii) the wavelength of the wave.

(b)Figure below shows the graph of the variation of the displacement of the same wave with time at a

partdisplacement/m 0.6

time/s 0 2.5

-0.6

State the values for :

(i) the time for one complete cycle.

(ii) The frequency of the wave.

(c) Calculate the speed of the wave drawn in the above figures.

1.2 ANALYSING REFLECTION OF WAVES.

WATER WAVES

Incident wavefrontsriCard board tubeStop watchSoft surface to absorb sound wave.EarFlat hard surface to reflect sound wave.SOUND WAVESLIGHT WAVESIncident light rayShiny smooth planeReflected light rayriDirection of reflected waveReflected wavefrontsNormalIncident raysReflected rays

LAWS OF REFLECTIONThe incident ray, the reflected ray and the normal all lie in the same plane.The angle of incidence is equal to the angle of reflection, i.e. i = r.

EFFECTS OF REFLECTION OF WAVEVelocity vRemain the same before and after reflectionsFrequency fWavelength

ASSESSMENT 1.2.

1.The diagram shows a light ray with an incident angle of 5 being reflected by a plane mirror MN. The mirror is then rotated clockwise through an angle of 15.

515

What is the new angle of reflection of the light ray? A 5 B 10 C 15 D 20

2. Which diagram shows the correct pattern of reflected water waves?

A BCD

STRUCTURED QUESTION.

1. When a wave is reflected from a plane surface, the angle of is equal to the

angle of .

2.If a ray of light strikes a plane surface at an angle of 45 to the normal, the angle of the reflected ray to

the normal is.

3. Sometimes while hiking, you may be able to hear your shout being reflected from a cliff. What is this effect known as, and what causes this to happen ?

4. Draw a diagram to show how a plane mirror reflects light waves from a lamp placed infront of it. (Follow the instructions listed below)(a) Draw a straight line perpendicular to the incident wavefronts to show the line of propagation of the wave.Show the direction of propagation.(b) Draw a dotted line which is perpendicular to the plane mirror to indicate the normal.(c) By using a protractor measure the angle of incidence i.(d) Then draw a line which is at an angle r from normal to represents the direction of propagation of reflected light waves.Note that i = r.(e) Draw straight dotted lines representing the reflected wavefronts which are perpendicular to the line drawn in (d).

LampPlanemirrorIncident wavefronts

ANSWER KEY.

Activity 1.1 (a)1.transverse wave, water wave.2.longitudinal wave, sound wave.3.(a) shake the spring from side to side. (b)shake the spring forward and backward.4. Energy in a transverse wave travels in a direction that is perpendicular to the direction of the vibrations.But energy in a longitudinal wave travels along the direction parallel to the direction of the vibrations.

Activity 1.1(b)1.in phase, wavefronts, plane wavefronts,circular wavefronts.2.(a) perpendicular, wavefronts. (b)

Activity 1.1(c)1.distance, crests, troughs, meter.2.complete, one, hertz.3. frequency, wavelength.4. period5. frequency.6. speed of wave7. 300 cms-18. displacement/cm Period T

Displacement/cm

amplitudamplitud

Distance/cmTime/s

Frequency f = Activity 1.1 (d)1.length,mass of bob.2.The vibrations will slow down and the amplitude will decrease.3. frequency, natural frequency.4.(a) It will vibrate with a maximum amplitude. (b) Resonance5.

ASSESSMENT.1.1OBJECTIVE:1A2C

3B4C

5D6C

7C8C

9D10A

STRUCTURED QUESTIONS.

1.Speed of wave, v = = f

Therefore t = = = 25 s

2.(a) Amplitude = = = 0.15 m

(b) Frequency ===2.5 Hz (c) Speed, v = f= 2.5 x 0.8 = 2.0 ms-1

3.a (i) 0.6 m (ii) 5.0 m b (i) 1.25 s(ii)0.80 Hz c Speed of the wave = Wavelength X Frequency = 5.0 x 0.8 = 4 ms-1

ASSESSMENT 1.2OBJECTIVE

2. D3. A

STRUCTURED QUESTION.

1. incidence, reflection.2. 453. LampPlanemirrorIncident wavefrontsreflection of sound wave or echo.4.

i r

4