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Wave and Sound


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waves


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A wave is a phenomenon in which energy is transferred through vibrations


Properties of waves:
1. The source of any wave is a vibration or oscillation.
2. Waves transfer energy from 1 point to another.
3. In waves, energy is transferred without the medium being transferred.

Transverse waves
  • Transverse waves are waves that travel perpendicular to the direction of motion.
  • Examples of such waves include rope waves and water waves.
  • The crest is the highest points of the wave whereas the trough is the lowest points of the wave.
Longitudinal waves
  • Longitudinal Waves are waves that travel parallel to the direction of motion.
  • Examples are sound wave and pressure waves.
  • They form compressions and rarefactions.
  • Compressions are region where the air particles are close together, creating high pressure.
  • Rarefactions are areas where the air particles are far apart, creating low pressure.
Wavelength
  • A wavelength is the shortest distance between any 2 corresponding points in a wave.
  • SI unit: metre.
  • Amplitude is the maximum displacement from the rest or centre position (high of a crest or depth of a trough).
  • SI unit: metre.
Period
  • This is the time taken for 1 point on the wave to complete 1 oscillation.
  • it is the time taken to produce 1 wave.
  •  The SI Unit is seconds (s).
Frequency
  • Frequency (f):It is the number of complete waves per second. 
  • the number of occurrences within a given time period. When there is a higher frequency, more waves are produced in 1 second, thus the period will be shorter.
  • SI unit: Hertz (Hz).
Wave speed
  • the distance of the wave moved in 1 second in the medium.
  • It is dependent of the medium itself.
  • For example, for sound, the wavespeed is always the same unless the medium is changed from solid to liquid.
  • measured in metre per second.
Wavefront
  • an imaginary line on a live that joints all points that are in the same phase.
  • It is usually drawn by joining the wave crests.
Reflection of waves
  • When water waves get reflected, the only thing that changes is the direction.
  • The wavelength, frequency and speed remains the same throughout.
  • Sponges are used to absorb the reflections of the water waves.
Refraction of waves
  • When water waves get refracted (move from deep to shallow water), the speed and the wavelength changes.
  • The frequency of the wave does not change
Electromagnetic Spectrum
  • Electromagnetic waves are transverse waves. They are electric and magnetic fields that oscillate at 90° to each other.
  • They transfer energy from one place to another.
  • They can travel through vacuum (do not require any medium to travel)
  • They travel at 3.0 x 108 per second in vacuum. They will slow down when travelling through water or glass.
  • The wave equation is applicable here too.
  • They obey the laws of reflection and refraction.
  • They carry no electric charge (they are neither positively or negatively charged)
  • Their frequencies do not change when travelling from one medium to another. Only their speeds and wavelength will change.

Most important equation

Speed = frequency x wavelength

Sound

  • Sound is a form of energy.
  • The energy is passed from 1 point to another as a wave.
  • Sound is an example of longitudinal wave.
  • Sound is produced by vibrating sources placed in a medium (air).
  • It travels in air through a series of compressions or rarefactions.
  • Compressions: Air molecules are close together, forms high pressure.
  • Rarefactions: Air molecules are far apart, forms low pressure.
Speed of sound differs in different medium

Air: 330 - 340m/s
Water: 1500m/s
Glass: 5000m/s

Speed of sound differs because:
  • Differences in strength of interatomic forces
  • Closeness of atoms in the 3 states
  • Temperature
- The Wave Equation can also be used to find the speed of sound
- The speed of sound is solids like metals are so fast that we can assume/ignore the time it takes to travel a distance.

Echoes
  • Echoes refer to the repetition of a sound resulting from reflection of the sound waves.
  • Echoes are formed when a sound is reflected off a hard and flat surface.
  • Reverberation occurs when the surface is too close, causing any reflected sound to follow closely behind the direct sound and prolonging the original sound.
Ultrasound
  • The range of frequencies which a person can hear is known as the range of audibility. 
    • Human: Between 20 Hz and 20 kHz
    • Dog: <20 kHz
    • Bats: Between 10 kHz and 120 kHz.
  • Ultrasound is the sounds with frequencies above the upper limit of the human range of audibility.
  • Its small wavelength means less diffraction and the echo formed is more precise in direction.
  • Applications for ultrasound include:
    • Determining depth of seabed
    • Locating sunken ships / shoals of fish
    • Cleaning small dirt from jewellery
    • Quality control (checking for cracks) in concrete
    • Medical applications (development of foetus)
Loudness
  • a factor distinguishing between various sounds.
  • The larger the amplitude of vibration, the louder the sound
  • Sound is measured by decibels (dB).
Pitch
  • a factor distinguishing various sounds
  • The higher the frequency of a note, the higher the pitch
  • Pitch is measured in hertz (Hz).

Bonus: Analogue and Digital Signals


Bonus: AM/FM Radio Transmission


MCQ Questions

1. Which of the following waves cannot pass through a vacuum?
a. light
b. sound
c. X-rays
d. radio waves

2. The distance between 2 successive wavefronts is equal to
a. half the distance between a crest and a trough
b. the distance between a crest and a trough
c. the distance between two successive crests
d. the distance between three successive crests

3. A ripple tank with a vibration hitting the surface of the water at a frequency of 50Hz produces 10 complete waves in a distance of 20cm. The velocity of water wave produced is
a. 0.1 m/s
b. 10 m/s
c. 1 m/s
d. 100 m/s

4. A crest of a water wave travels 40cm in 5s. If the distance between 2 successive crests is 5mm, what is the frequency of the wave?
a. 0.2 Hz
b. 1.6 Hz
c. 8 Hz
d. 16 Hz

5. In a ripple tank, circular waves are reflected from a straight barrier. Which one of the following shapes best describes the shape of the reflected waves?
a. circular
b. planar
c. parabolic
d. square

6. Which one of the following is changed when the wave is reflected?
a. wavelength
b. frequency
c. speed
d. velocity

7. Which of the following is not changed when the wave is refracted?
a. wavelength
b. frequency
c. speed
d. velocity

8. All electromagnetic waves in vacuum have the same
a. amplitude
b. frequency
c. wavelength
d. velocity

9. Which of the following waves has the longest wavelength?
a. gamma rays
b. infra-red
c. ultraviolet
d. X-rays

10. A dipper dips into the water in a ripple tank at a frequency of 20 Hz produces plane water waves which travel at a speed of 40cm/s. What is the wavelength of the waves?
a. 0.02m
b. 2m
c. 40m
d. 800m

11. A wave source of frequency 2000Hz emits waves of wavelength 0.2m. How long does it take for the waves to travel 4000m?
a. 0.4s
b. 0.5s
c. 2s
d. 10s

12. Two notes are played on a piano. The second note is louder and has a lower pitch. The second note is
a. higher in amplitude and higher in frequency
b. higher in amplitude and lower in frequency
c. lower in amplitude and higher in frequency
d. lower in amplitude and lower in frequency

13. An instrument on a ship that is used to measure the distance between the ship and a cliff sends out a pulse of sound and receives an echo 5s later. If the speed of sound in air is 330m/s, how far is the ship from the cliff?
a. 66m
b. 825m
c. 1650m
d. 3300m

14. During a thunderstorm, an observer sees a lightning flash. 6 s later he hears the thunder. The speed of sound is 330m/s. Approximately how far away is the observer from the lightning?
a. 1/20 km
b. 1/3 km
c. 1/2 km
d. 2 km
e. 30km

15. A dolphin emits an ultrasonic wave with a frequency of 150 000Hz. The speed of the ultrasonic wave in water is 1500m/s. What is the wavelength of this wave in water.
a. 0.0001m
b. 0.01m
c. 0.1m
d. 10m
e. 100m

16. A marine survey ship sends a sound wave straight to the seabed. It receives an echo 1.5s later. The speed of sound in seawater is 1500m/s. How deep is the sea at this position?
a. 500m
b. 1000m
c. 1125m
d. 2250m
e. 4500m

17. Water waves were produced in a ripple tank using a vibrator of frequency 3Hz. Which of the following values of speed and wavelength could the waves have had?
a. speed = 1cm/s; wavelength = 3cm
b. speed = 2cm/s; wavelength = 1cm
c. speed = 5cm/s; wavelength = 15cm
d. speed = 6cm/s; wavelength = 3cm
e. speed = 12cm/s ; wavelength = 4cm

18. A surf board moves at 5m/s on the crest of a wave. The distance between wave crests is 10m. The frequency of the wave motion is
a. 0.5Hz
b. 1Hz
c. 2Hz
d. 5Hz
e. 10Hz


19. Which of the following cannot travel through glass?
a. ultraviolet waves
b. water waves
c. sound waves
d. light waves


20. Which of the following is a property of electromagnetic waves?
a. they are reflected by mirror only
b. they travel at a speed of 330m/s through air
c. they are deflected by magnet
d they can travel through a vacuum


21. The figure shows a sea-wave that causes a small cork (z) to rise up and down through one complete oscillation every 4 seconds. Refer to this for questions 21 to 23.
The amplitude of the wave is
a. 0.5m
b. 1.0m
c. 1.5m
d. 3.0m

22. The horizontal speed of the wave is
a. 0.25m/s
b. 0.75m/s
c. 4m/s
d. 12m/s

23. If the wave is moving to the right, after 4 seconds the cork z will be at position
a. P
b. Q
c. R
d. S

24. A large ripple tank with a vibrator working at a frequency of 30 Hz produces 25 complete waves in a distance of 50cm. The velocity of the wave is
a. 1500cm/s
b. 750cm/s
c. 60cm/s
d. 5/3 cm/s

25. A source of frequency 500 Hz emits waves of wavelength 0.2m. How long does it take the waves to travel 600m?
a. 3s
b. 6s
c. 12s
d. 60s

26. A wave of frequency 1000 Hz travels between two points P and Q with a velocity of 300m/s. How many wavelengths are there in PQ if the length of PQ is 600m?
a. 0.3
b. 3.3
c. 600
d. 2000

27. Which one of the following statements about ultraviolet radiation and visible light is not true?
a. they are emitted by the sun
b. they have the same frequency
c. the vibrate transversely
d. they can be reflected by polished sheets of metal

28. A VHF radio station broadcasts at a frequency of 100 MHz (1.0 x 108 Hz). The speed of radio waves is 3.0 x 108 m/s. What is the wavelength of the waves broadcast by the station?
a. 0.33m
b. 3.0m
c. 4.0 x 1015m
d. 3.0 x 1015m

29. Which of the following is an example of longitudinal wave?
a. blue light
b. water ripples
c. radio wave
d. sound wave

30. A boy, using a stopwatch, notes that there is a 3s delay between the flash of lighting and the sound of thunder. How far is he from the thunderstorm? Assume speed of sound is 330m/s
a. 990m
b. 110m
c. 3.3km
d. 1.1km

31. Which type of electromagnetic radiation travels at the highest speed through a vacuum?
a. gamma rays
b. light waves
c. radio waves
d. none - all travel at same speed

32. Sound waves cannot be sent from earth to the moon because
a. sound waves are stationary waves
b. sound travels too slowly
c. the distance between the earth and moon is too far
d. there is a vacuum between the earth and the moon

33. Dolphins communicate with one another mainly by means of sound...
a. travelling through the water
b. travelling through the seabed
c. reflected from the water surface
d. reflected from the sea bed

34. Sound in air causes the formation of
a. rarefactions or compressions
b. rarefactions and compressions
c. crests or troughs
d. crests and troughs

35. Frequencies of sound which can be heard by the human ear are called
a. audible frequencies
b. auxillary frequencies
c. normal frequencies
d. low frequencies

36. We can hear sounds of frequencies between
a. 10 Hz and 10 kHz
b. 10 Hz and 20 kHz
c. 20 Hz and 20 kHz
d. 20 Hz and 10 kHz

37. The minimum frequency of ultrasonic sounds is
a. 10 Hz
b. 20 Hz
c. 10 kHz
d. 20 kHz

38. When sound passes through wood, the particles of the wood oscillate
a. parallel to the direction of the sound
b. perpendicular to the direction of the sound
c. at 45º to the direction of the sound
d. up and down

39. When the amplitude of a sound increases, the
a. wavelength of the sound increases
b. speed of the sound increases
c. pitch of the sound increases
d. loudness of the sound increases

40. Hitting a drum louder produces a louder sound which is caused by the increased
a. wavelength
b. frequency
c. speed
d. amplitude

41. Noise which is harmful to our ears has levels above
a. 8 dB
b. 80 dB
c. 800 dB
d. 8000 dB

42. A sonar signal is a sound wave having
a. low frequency
b. high frequency
c. a single frequency
d. various frequencies

43. Which one of the following musical instruments produces notes of the highest quality?
a. violin
b. guitar
c. drum
d. piano

44. The quality of a note depends on its
a. frequency
b. wavelength
c. amplitude
d. waveform

45. A man's voice is usually different from a woman's voice mainly due to the difference in their
a. pitch
b. quality
c. loudness
d. wavelength

46. Which one of the following quantities of a sound is changed when the sound is reflected?
a. wavelength
b. period
c. frequency
d. direction of motion

47. A student, using a stopwatch, notes that there is a delay of 4s between the flash of lightning and the sound of thunder. How far is the student from the lightning and thunder? (Assume speed of sound in air is 330 m/s)
a. 82.5m
b. 165m
c. 660m
d. 1320m

48. When a teacher is talking in an enclosed air-conditioned room, the students do not hear echo because
(1) the wall is not big enough
(2) sound travels too fast
(3) the sound energy is absorbed by the students and furniture

a. (1) and (2) only
b. (1) and (3) only
c. (2) and (3) only
d. (1), (2) and (3)

49. Which of the following statements is/are true about sound?
(1) A loud sound travels faster than a soft sound
(2) A high pitch sound travels faster than a low pitch sound
(3) A sound with short wavelength has a high pitch than a sound with a longer wavelength

a. (3) only
b. (1) and (2) only
c. (1) and (3) only
d. (1), (2) and (3)

50. Ships use sound waves to find the vertical distance to the seabed. A pulse of sound waves is sent out and the echoes are detected. A ship emits a pulse of waves lasting 0.50s. The waves have a frequency of 3600Hz. How many complete wavelengths does the pulse contain?
a. 1800
b. 3600
c. 7200
d. 18 000

51. A sound is played on a flute. A sound of the same pitch is played on a trumpet. Which of the following correctly compares the two sound waves?
        frequency        speed
a.    different            different
b.    different            same
c.    same                different
d.    same                same

MCQ Answers

1. b
2. c
3. b
4. d
5. a
6. d
7. b
8. d
9. b
10. a
11. d
12. b
13. b
14. d
15. b
16. c
17. e
18. a
19. b
20. d

21. a
22. b
23. d
24. c
25. b
26. d
27. b
28. b
29. d
30. a
31. d
32. d
33. a
34. b
35. a
36. c
37. d
38. a
39. d
40. d
41. c
42. b
43. d
44. d
45. a
46. d
47. d
48. c
49. a
50. a
51. d

Structured Question Worked Solutions

1. A gramophone record was made to play at 45 r.p.m. Explain why the frequency of the notes heard is decreased when the record is played at a speed of 33 1/3 r.p.m

Solution


1. As the wavelength of the notes are recorded permanently on the record, a reduction in speed reduces the frequency of the notes heard.


2. Name the part of the electromagnetic spectrum as described in the following
a. its wavelengths are shorter than those of visible light and it is used to treat cancer

b. its frequencies are lower than those of visible light and it is reflected by layers in the upper atmosphere during its transmission

c. its wavelengths are shorter than those of visible light and it is used to detect cracks in lead beams

d. its frequencies are higher than those of visible light and it is absorbed by glass to produce fluorescence

Solution

2a. gamma rays
2b. radio waves
2c. X-rays
2d. ultraviolet rays



3. The speed of light in air is 3.00 x 108 m/s. The speed of sound in air in 0.34km.s. An observer is 5.00km away from the lightning discharge.

a. calculate the travel time to the observer of
i. light from the lightning flash
ii. sound from the thunder

b. what is the time interval between the observer seeing the lightning and hearing the thunder?

Solution

3ai. travel time to the observer of the light from the lightning = 5000 / (3 x 108) = 1.67 x 10-5 s
3aii. travel time to the observer of the sound from the thunder = 5000/340 = 14.7 s

3b. time interval = 14.7 s



4.
A student sits in the middle of a rectangular hall which is 17m wide, as shown above. When the student hits a drum, two echoes are heard, 50 ms and 80 ms respectively, after the bang.

Assuming that there is no echo from the ceiling, calculate
a. the speed of sound in air
b. the length of the hall

Solution

4a. consider the first echo, where the sound travelled a distance of 17m in the time 50 ms (0.05s)
Speed = 17/0.05 = 340 m/s

4b. distance = time x speed = 0.08 x 340 = 27.2
length of hall = 27.2 m



5a. A loudspeaker and microphone are set up facing each other several metres apart. Explain how the vibrations of the cone of the loudspeaker produce sound waves in the air and how these waves are transmitted through the air to the microphone

5b. The separation of the loudspeaker and the microphone in (a) is 6.8m. When the cone of the loudspeaker vibrates at a frequency of 200Hz, there are exactly 4 complete waves in the air between the loudspeaker and microphone

i. calculate the speed of sound as it travels in the air between the loudspeaker and microphone
ii. estimate the number of waves between the loudspeaker and microphone when the frequency of 2.00kHz
iii. state the effect on the sound heard by a normal healthy ear if the frequency is changed from 200Hz to 2.00kHz

Solution

5a. When the cone of the loudspeaker vibrates, the layer of air molecules next to the cone also vibrates at the same frequency. When the cone moves to the right, the layer of air molecules nearest to it is compressed, forming the compression.

When the cone moves to the left, the layer of air molecules nearest to it is pulled further apart forming the rarefaction.

Hence as the cone vibrates, a series of alternate compressions and rarefactions travels outwards from the cone of the loudspeaker which is along the same direction as the vibration of the cone. Thus the sound wave is transmitted through air to the microphone

5bi. wavelength = distance / number of waves = 6.8 / 4 = 1.7m
speed of sound = frequency x wavelength = 200 x 1.7 = 340 m/s

5bii. the speed of sound in air remains constant. Frequency of a sound wave is inversely proportional to its wavelength. The sound of a frequency of 2000Hz is 10 times higher than that of sound at a frequency of 200Hz. The corresponding wavelength of the sound wave at a frequency of 2000Hz is reduced to 10 times smaller than 1.7m. Since the distance between the loudspeaker and microphone remains unchanged, the number of waves is thus increased by 10 times to 40.

5biii. when sound at a frequency of 200Hz is produced, a lower pitched humming sound is heard. As the frequency of the sound is increased to 2000Hz, a higher pitched sound is heard.



6.
The diagram shows a metal rod, 2.4m long, being struck a sharp blow at one end using a light hammer. The time interval between the impact of the hammer and the arrival of the sound wave at the other end of the rod is measured.

Four measurements of the time interval are 0.44ms, 0.50ms, 0.52ms, and 0.47ms

a. Determine the average value of the four measurements
b. Hence, calculate a value for the speed of sound in the rod.

Solution

6a. 0.00048s
6b. 2.4 / 0.00048 = 5000m/s



7a. The sound wave from a source of frequency 400Hz travels in air at a speed of 340m/s. Calculate the wavelength of this sound wave

7b. At any instant there are compression and rarefactions along the path of the sound wave

i. explain briefly the meaning of compression and rarefactions
ii. what is the distance from the centre of a compression to the centre of the nearest rarefaction in the wave described in a?

Solution

7a. 0.85m

7bi. at compression, the air molecules are brought closer than that in normal positions. At rarefaction, the particles are further apart than in their normal position

7bii. 0.425m



8.

The figure shows a boy setting up waves on a long elastic cord. The student's hand makes one complete up-and-down movement in 040s, and in each up-and-down movement the hand moves through a height of 0.30m. The wavelength of the waves on the string is 0.80m

For this wave, find the
a. amplitude
b. frequency
c. speed


[0.15m; 2.5Hz; 2m/s]


9. A source of frequency 500 Hz emits waves of wavelength 0.2m. How long does it take the waves to travel 400m?

[4s]


10. A wave of frequency 500 Hz travels between two points P and Q with a velocity of 300m/s. How many wavelengths are there in PQ if the length of PQ is 600m?

[1000]


11. A vibrator of frequency 3 Hz produces waves with an amplitude of 0.5m and a wavelength of 12cm. What is the velocity with which the waves travel across the surface?

[36cm/s]


12. A stick dips steadily into a pond 30 times each second. 50 complete waves are counted on the water surface over a distance of 1m. How fast is the wave travelling?

[60cm/s]


13. A gun is fired between two parallel vertical walls. The echo from one wall is heard after 0.1s; the echo from the other wall is heard after 3.0s later. How far apart are the walls if the speed of sound in air is 340m/s?


[680m]

14. A popular speaker is addressing a very large crowd of people. The public address loudspeakers are mounted on the front of the speaker's platform. The speech is also broadcast by radio. An observer in the crowd notices that he receives the radio broadcast on his radio 1.6s before he hears the same word from the loudspeakers. Estimate the distance of the observer from the platform. State any assumption that you make in arriving at your estimate.
(take speed of sound in air to be 330m/s)

Solution

Distance of observer from platform = time x speed of sound = 1.6 x 330 = 528m

It is assumed that there is no wind and the time lapse between the time the sound leaves the radio and enters the ear is negligible.

15. The echo finder of a ship sends a pulse of ultrasound wave vertically downwards to the seabed and detects the echo 2.4s later.
a. Estimate the speed of sound in water.
b. Estimate the depth of the water.

Solution

15a. speed of sound in water is approximately 1500m/s
15b. 2 x depth = speed x time
depth = (1500 x 2.4) / 2
depth of water = 1800m

16. A hammer strikes one end of a 600m long metal pipe. A sensitive sound detector at the other end detects two sounds at an interval of 1.9s between them. The speed of sound in air is 300m/s.
a. Calculate the time taken for the sound to reach the detector by air.
b. Calculate the speed of sound in the metal pipe.

Solution

16a. time taken through air = distance/speed
600/300 = 2.0s
16b. time taken through metal pipe = 2.0 - 1.9 = 0.1s
speed of sound in pipe = distance/time = 600/0.1 = 6000m/s

17. A man P faces a vertical wall which is 400m from him. A second man Q stands 100m in front of P. When P fires a gun, Q hears two reports.
a. Why does Q hear two reports?
b. State two characteristics of the wall which cause Q to hear the second report.
c. What is the time interval between the two reports if the velocity of sound is 320m/s

Solution

17a. The first report is the direct sound from the gun to man Q. The second report is caused by the echo when the sound hits the wall.
17b. The echo from the wall is possible when the wall surface is big and the wall is hard.
17c. The extra distance travelled by the echo = 2 x 300 = 600m
Time interval between gunshot and echo = distance/speed = 600/320 = 1.88s
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