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Physics

National 4/5

L e s m a h a g o w H i g h S c h o o l

Waves and RadiationWave Parameters, Behaviours and CharacteristicsExtra Question Booklet

Nat

FrequencyIn this section you can use the equation:

where frequency is measured in Hertz (Hz)time is measured in seconds (s).

1. Find the missing values in the following table.

Frequency (Hz) Number of Waves

Time (s)

(a) 10 5

(b) 30 60

(c) 800 3 200

(d) 12 9 600

(e) 50 90

(f) 20 000 15

2. If a wave machine produces 5 waves each second what is the frequency of the machine?

3. A man stands on a beach and counts 40 waves hitting the shore in 10 seconds. What is the frequency of these waves?

4. In 100 seconds a particular smoke alarm emits 1,000,000 sound waves. What is the frequency of the sound waves?

5. A girl is sitting on the edge of a pier. It takes 0·625 seconds for one complete wave to pass underneath her. What is the frequency of the waves?

6. A girl stands on a beach and counts 15 waves crashing onto the shore in a time of 1 minute. What is the frequency of the waves?

7. A rock is thrown into a pond and an overhead photograph is taken 2 seconds later. The photograph, as shown in the

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number of wavestime taken

= Frequency

Frequencydiagram below, reveals that 5 waves were produced in the 2 second period.

What was the frequency of these water waves?

8. In a swimming pool a wave machine creates waves with a frequency of 2 Hz. How many waves are produced in 5 minutes?

9. A smoke alarm sends out high-pitched sound waves with a frequency of 12,000 Hz. If the alarm is on for 30 seconds how many waves does it emit?

10. A pebble was thrown into a still pond and wave ripples were produced at a rate of 3 waves per second.The diagram below represents the wave pattern in the pond a

short time after the pebble was dropped.

(a) What was the frequency of the waves, in Hertz?(b) How many waves are represented in the diagram

above?(c) How long did it take for this wave pattern to form?

11. An oil tanker is anchored off Gulberwick. A crew member on board counts 15 waves passing him in one minute. Calculate the frequency of the waves in hertz.

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E .g.

Wavelength

Helpful Hint Wavelength ( symbol ) means the length of a wave. It is measured as the distance from one point on a wave to an identical point on the next wave.

1. ‘A-B’ represents one wavelength in the diagram below.

State two other pairs of letters which represent one wavelength.

2. How many waves are shown in each of the diagrams below?

3. The wave train shown below is 20 metres long. How long is each wave?

4. The wavelength of the waves in the diagram below is 3 cm. What is the distance between X and Y?

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(a)

(d)(c)

(b)

Wavelength

5. What is the wavelength of the waves in the diagram below?

6. Draw a wave train consisting of 2 waves. Put the labels wavelength and amplitude on your diagram in appropriate places.

7.

(a) How many waves are shown in the diagram above?(b) What is the wavelength of each of these waves?

8. (a) Calculate the wavelength of the waves shown below.

(b) What is the distance from X to Y in this wave train?

9. A stone is thrown into a pond, and a wave pattern is produced as shown below. The wavelength of the waves is 6 cm.


X Y

X

Y

Wavelength

Calculate the distance, d, travelled by the outside wave.

10. Red light from a laser has a wavelength of 4 x 10-7 m in a certain glass. How many waves, from this laser, would cover a length of 2 cm in this glass?


d

Speed of a Wave 1In this section you can use the equation:

speed = frequency x wavelength

also written as

v = f

where v = speed of the wave in metres per second (m/s)f = frequency in Hertz (Hz)= wavelength in metres (m).

1. Find the missing values in the following table.

Frequency (Hz) Wavelength (m) Speed (m/s)

(a) 5 3

(b) 50 0·02

(c) 2 0·5

(d) 20 000 340

(e) 20 600

(f) 5·5 x 10-7 3 x 108

2. Water waves in a swimming pool are travelling with a speed of 2 m/s and have a wavelength of 0·8 m. What is their frequency?

3. The musical note ‘E’ has a frequency of 320 Hz. If sound travels with a speed of 340 m/s in air calculate the wavelength of this sound in air.

4. Sound of frequency 440 Hz has a wavelength of 3·41 m in water. Calculate the speed of sound in water.

5. What is the speed of waves which have a frequency of 50 Hz and a wavelength of 3 m?

6. A wave machine in a swimming pool produces waves with a frequency of 1 Hz. If they travel across the pool at 1·5 m/s

what is their wavelength?


Speed of a Wave 17. A wave generator in a ripple tank creates waves which have a

wavelength of 0·02 m. If the speed of these waves is 1·2 m/s what is their frequency?

8. The speed of sound in steel is 5200 m/s. What is the wavelength of a sound wave which has a frequency of 6500 Hz in steel?

9. How fast will waves with a frequency of 15 000 Hz and a wavelength of 2·2 cm travel?

10. What is the wavelength of waves which have a frequency of 6 x 106 Hz and a speed of 1800 m/s?

11. Waves produced by a wave generator in a ripple tank have a wavelength of 16 mm. At what frequency is the wave

generator operating if the wave speed is 0·64 m/s?

12. Calculate the frequency of the waves shown in the diagram below given that they have a speed of 0·05 m/s.

13. A boy counts 40 complete waves along the length of a swimming pool. The pool is 50 m long and the waves are travelling with a speed of 3·75 m/s. Calculate:

(a) the wavelength of the waves(b) the frequency of the waves(c) the number of waves produced in 1 minute.


1 mm

Speed of a Wave 114. Waves, like the ones shown in the diagram below, are produced at a rate of 8 000 Hz. Calculate the speed of these waves.

15. A wave pattern formed 3 seconds after a pebble is dropped into a pond is shown below.

(a) How many waves were formed in 3 seconds?(b) What was the frequency of the waves?(c) What was the wavelength of the waves?(d) Calculate the speed of the waves.

16. 30 water waves per second are created in a pool. Some of these are represented in the diagram.

(a) State the wavelength of the waves. (b) Calculate the wave speed.

17. The waves shown in the diagram below were produced at a rate of 30 waves per minute.

(a) What is their frequency? (b) What is their wavelength? (c) Calculate the speed of these waves

18. The diagram below represents some water waves coming onto shore.


0·3 m

12

28 cm

9

Speed of a Wave 1

A girl standing on the shore counts 36 wave crests crashing onto the shore in 1 minute. Calculate the frequency, wavelength and speed of these waves.

Helpful Hint Remember! When dealing with waves, you can also use the equation

19. It takes 25 seconds for a wave in a swimming pool to travel from one end of the pool to the other end. The wave has a frequency of 2·5 Hz and its wavelength is 0·4 m.

(a) What is the speed of the wave?(b) What is the length of the pool?

(a) Calculate the speed of the sound waves.(b) Calculate the wavelength of the sound waves.

21. A wave generator in a ripple tank creates waves, which have awavelength of 2·5 cm, at a rate of 6 waves per second.

The ripple tank is 60 cm long.

(a) What is the frequency of the waves?(b) Calculate the speed of the waves.(c) How long will it take for a wave to travel the length of

the ripple tank?


2·7 m

speed = distance

time

20. An alarm is set off creating sound waves of frequency 10 000 Hz. It takes 0·6 seconds for the sound to reach a man who is standing at a distance of 204 m from the alarm.

Speed of a Wave 122. Waves of frequency 8·1 x 105 Hz can travel a distance of 27 000 m in a time of 9 x 10-5 seconds. What is the wavelength of these waves?

23. An athlete is working on her hurdling technique with her trainer The trainer stands some distance up the track and blows

his whistle, sending out 8 500 Hz sound waves which have a wavelength of 4 cm. It takes 0·22 seconds for the sound waves to reach the athlete.

Calculate the starting distancebetween the athlete and her trainer.

24. Consider the waves in the following diagram:

(a) What is the wavelength of these waves?(b) Calculate the speed of the waves given that it takes

0·001 s for one complete wave to pass a point.(c) Calculate the frequency of the waves.(d) How many of these waves would pass a point in 1

minute?

25. The pond waves represented in the diagram below have a frequency of 24 Hz and a wavelength of 10 cm. The pattern was formed by dropping a stone into the water.

(a) Calculate the speed of the waves.(b) How long did it take for this pattern to form from the

moment the stone made contact with the water?


24 cm

Speed of a Wave 21. On 14 February 1876 Alexander Graham Bell registered his

invention, the telephone at the patent office. The modern telephone is based on his original invention.The handset of a telephone contains a microphone and a

loudspeaker

(a) Telephones are linked together by wires. Give two advantages of communicating through wires rather than through the air.

(b) What energy change takes place in the microphone? (c) What energy change takes place in the loudspeaker? (d) How fast does a signal travel along a telephone wire?

2. Look at the diagram of a water wave below.

(a) How many waves are shown in the diagram?(b) What is the wavelength of the waves?(c) What is the amplitude of the waves?(d) The wave travels a distance of 24 m in 8 seconds. What

is the speed of the wave?(e) Calculate the frequency of this water wave.


1·8 m

35 cm

Speed of a Wave 2

3. A schoolboy, who is studying waves in school, decides to put some theory into practice. He stands at the edge of a loch, near a harbour, and waits for a large car ferry to pass by on its way out of the loch. The boy has a stop clock and a metre stick for his investigation.

As the car ferry passes by it creates large waves and the boy notices that 20 waves strike the shore in 12 seconds and that

the first wave takes 10 seconds to reach the shore. The boy then records the time interval between waves and also the approximate distance between successive wave crests. His results are shown below.

Time for 1st. wave to reach shore from boat........12 seconds.

Distance between 2 successive wave crests......1·8 metres. Number of waves striking the shore in 12 seconds.........20

(a) What was the frequency of the waves produced by the car ferry?

(b) What was the wavelength of the waves produced by the car ferry?

(c) Calculate the speed of the waves.(d) How far was the car ferry from the shore?


Speed of a Wave 31. Thunder is heard 20 seconds after a lightning flash. If the

speed of sound is 340 m/s, how far away is the storm?

2. Explain why, during a thunder storm, you see the lightning before you hear the thunder.

3. On a day when the speed of sound in air is 330 m/s, how long would sound take to travel a distance of 1.6 km?

4. During a thunder storm it is noticed that the time interval between the flash of lightning and the clap of thunder gets less. What does this tell you about the storm?

5. Describe a method of measuring the speed of sound in air giving:

a) the apparatus usedb) the measurements takenc) any equations used in the calculation.

6. Ten pupils are standing on Calton Hill, looking at Edinburgh Castle. They measure the time difference between seeing the smoke from the one o’clock gun and hearing the bang.The measured times are 3.8 s, 4.2 s, 4.0 s, 3.8 s, 4.4 s, 3.8

s, 4.0 s, 4.2 s, 3.6 s, and 4.2 s.

a) Calculate the average time for the group.b) Calculate the distance from the Castle to Calton Hill if the speed of sound is 330 m/s.

7. An explosion in Grangemouth could be heard in South Queensferry one minute later .Given they are 20 km apart, calculate the speed of sound in air.

8. On a day when the speed of sound is 330 m/s, how long would the sound take to travel a distance of 19.8 km?

9. In a race the runners are at different distances away from the starter. They will hear the starting horn at different times. Using the speed of sound as 340 m/s, calculate the time difference in hearing the horn for two runners who are 5 m and 15 m from the starter.

10. Calculate how long it would take light to travel from the sun to the earth, a distance of 1.49 x 108 km.

11. How long will it take a radio signal to travel from Britain to Australia, a distance of 1.8 x104 km.

Physics: Mechanics and Heat (Int 2) – Student Material 14

Speed of a Wave 3


Types of wave1. What is carried from place to place via a wave?

2. a) Explain, using a diagram, the difference between atransverse and longitudinal wave.

b) What type of waves are the following:i) sound wavesii) water wavesiii) light waves.

3. Explain, using the particle model, why sound travels quicker in metals than gases.

4. Explain why sound cannot travel through a vacuum.


Speed, frequency, wavelength and period 1

1. The diagram below represents a wave 0.2 s after it has started.

Calculate the following quantities for this wave:a) wavelengthb) amplitudec) frequencyd) speed.

2. A swimming pool is to have a wave-making machine installed. The time taken for a wave to travel the length of the 50 m pool has to be 20 s and the wavelength has to be 4 m.

a) Calculate the speed of the waves.b) Calculate the required frequency of the waves.

3. Wave A has a wavelength of 6 cm and a frequency of 50 Hz. Wave B travels 250 m in 1 minute 40 s. Which wave travels faster - and by how much?

4. 40 waves are found to pass a point in 20 s. If the waves have a wavelength of 0.015 m, calculate their speed.

5. Calculate the wavelength of a wave of frequency 0.1 Hz and speed 5 m/s.

6. State what is meant by the period of a wave.

7. If the speed of a water wave is 0.6 m/s and the wavelength of each wave is 6 cm, calculate

a) the frequencyb) the period of the wave.



8. Waves of wavelength 5 cm travel 120 cm in one minute.Find their

a) speedb) frequencyc) period.

9. A sound generator produces 25 waves every 0.1 s. If the speed of sound is 330 m/s, find:

a) the wavelength of the soundb) the period of the wave



1. A swimming pool wave machine produces waves with a frequency of 0.7Hz. How many waves are produced in one minute?

2. A microphone picks up a sound wave with a frequency of 200Hz. How many waves will it pick up in a period of 12 seconds?

3. A particular colour of violet light has a wavelength of 500 nm. How many wavelengths fit into a one millimetre length?

4. Complete the missing values in the tableFrequency

(Hz)Wavelength

(m)Speed (m/s)

a 4 6b 10 9c 6 x 1014 5 x 10-9

d 4.5 x 10-9 3 x 108

e 4.5 x 10-9 2x 108

f 4 30g 800 340h 2000 340i 5.7 x 1014 3 x 108

5. What is the speed of light in a vacuum?

6. What is the typical speed of sound in air?

7. Can sound waves travel through:(a) metal? (b) water? (c) vacuum?

SIC Development Group CMcG 19

AmplitudeWavelength

Numerical SolutionsFrequency P2, 31. (a) 2 Hz

(b) 0.5 Hz(c) 4 s(d) 800 s(e) 4 500(f) 300 000

2. 5 Hz3. 4 Hz4. 10,000 Hz5. 1.6 Hz6. 0.25 Hz7. 2.5 Hz

8. 6009. 360,000 10. (a) 3 Hz

(b) 6 (c) 2 s

11. 0.25 Hz

Wavelength P 4-6

1. CE, FG2. (a) 3

(b) 2 (c) 4 (d) 2.5

3. 5 m4. 15 cm5. 40 m6.

7. (a) 12 (b) 2 m

8. (a) 12 m (b) 96 m9. 18 cm10. 50 000

Speed of a wave 1 P 7 - 111.(a) 15 m/s (b) 1 m/s (c) 0.25 m (d) 0.017 m (e) 30 Hz (f) 5.45 x 1014 Hz2. 2.5 Hz3. 1.06 m4. 1500 m/s5. 150 m/s6. 1.5 m7. 60 Hz8. 0.8 m9. 330 m/s10. 3 x 10-4 m11. 40 Hz

12. 50 Hz13.(a) 1.25 m (b) 3 Hz (c) 180 14. 2 400 m/s15.(a) 6 (b) 2 Hz (c) 2 cm (d) 0.04 m/s16.(a) 7 cm (b) 2.1 m/s17.(a) 0.5 Hz (b) 1.8 m (c) 0.9 m/s18. 0.6 Hz, 0.9 m,

0.54 m/s.19.(a) 1 m/s (b) 25 m20.(a) 340 m/s (b) 0.034 m21.(a) 6 Hz (b) 0.15 m/s (c) 4 s22. 370.37 m23. 74.8 m24.(a) 4 cm (b) 40 m/s (c) 1 000 Hz (d) 60 000 25.(a) 2.4 m/s (b) 0.25 s

Speed of a wave 2 P 12-131. (a) privacy, signal can travel further, Any other suitable answer (b) sound to electrical (c) electrical to sound (d) close to 3 x 108m/s

2. (a) 5 3. (a) 1.67 Hz (b) 7 cm (b) 1.8 m (c) 0.9 m (c) 3.0 m/s (d) 3 m/s (d) 36 m (e) 42.86 Hz

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Numerical Solutions

Speed of a wave 3 P 14 – 151. 6800m2. The speed of light is much faster than the speed of sound3. 4.85s4. The storm is getting closer5. a) Two microphones connected to a fast timer, a metre

stick, a hammer and something metallic to hit.b) Measure the distance between the microphones using a

metre stick.Measure the time taken for the sound to travel between

the timers using the fast timer. c) speed of sound = distance /time6. a) 4s b) 1320m7. 333m/s 8. 60s

9. 0.029s10. 497s


Particle travel

wave travel

Particle travel

wave travel

Numerical SolutionsTypes of Wave P16

1. a) longitudinal wave the particles move in the same direction as the wave travels.

Transverse wave the particles move at right angles to the direction of wave travel.

b) i) longitudinalii) transverseiii) transverse

2. Sound travels through metals faster than gases because most metals are solids at room temperature. The particles in a solid are packed closely together and can pass on sound vibrations easily. The particles in a gas are far apart and do not collide as easily.

3. Sound cannot travel through a vacuum because there are no particles to transfer the vibrations.

Speed, Frequency, Wavelength and Period 1 P17 - 18

1. (a) 1m (b)

0.015m (c) 20Hz (d) 20 m/s

2. (a) 2.5 m/s(b) 0.625 Hz

3. A by 0.5 m/s4. 0.03 m/s

5. 50m6. The period

of a wave is the time taken for one complete wave to pass a point

7. (a) 10 Hz(b) 0.1s

8. (a) 0.02m/s(b) 0.001Hz(c) 1000s

9. (a) 1.32m(b) 0.004s

Speed, Frequency, Wavelength and Period 2 P 191. 422. 24003. 20004. (a) 24 m/s


Numerical Solutions(b) 90 m/s(c) 3 x 106 m/s(d) 6.67 x 1016 Hz(e) 4.44 x 1016 Hz(f) 7.5 Hz(g) 0.425m(h) 0.17m(i) 5.26 x 10-7m

5. 3 x 108 m/s6. 340 m/s7. (a) Yes

(b) Yes(c) No


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