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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 7.15 Practice, Study, and Apply - Waves

Subsection Practice

Calculation 7.15.1. Wave Speed.

The speed of a wave in a medium depends on which of the following quantities?
  1. The amplitude of the source
  2. The frequency of the source
  3. The period of the source
  4. The characteristics of the medium
  5. The power of the wave
Answer.
D.

Calculation 7.15.2. Wave Frequency.

The frequency of a wave depends on which of the following quantities?
  1. The amplitude of the source
  2. The frequency of the source
  3. The period of the source
  4. The characteristics of the medium
  5. The power of the wave
Answer.
B., E.

Calculation 7.15.3. Wave Amplitude.

The amplitude of a wave depends on which of the following quantities?
  1. The power coming from the source
  2. The frequency of the source
  3. The period of the source
  4. The characteristics of the medium
  5. The wavelength of the wave
Answer.
A.

Calculation 7.15.4. Two Wave.

Waves A and B are traveling in the same medium, and they have the same wavelength and frequency. But Wave A has an amplitude twice that of Wave B. How does the speed of Wave A compare to the speed of wave B?
  1. The speed of Wave A is 1/4 the speed of Wave B.
  2. The speed of Wave A is 1/2 the speed of Wave B.
  3. The speed of Wave A is the same as the speed of Wave B.
  4. The speed of Wave A is twice the speed of Wave B.
  5. The speed of Wave A is four times the speed of Wave B.
  6. None of the above are correct.
Answer.
C.

Calculation 7.15.5. Wavelength of the Ocean.

Sitting on the dock of the bay, you notice that the crests of an ocean wave pass a pier every \(12.0 \mathrm{~s}\text{.}\) You know also that there are two buoys \(28 \mathrm{~m}\) apart, and that the crest travels between the buoys in about \(5 \mathrm{~s}\text{.}\) What is the wavelength of the ocean wave?
  1. 16.8 m
  2. 24.7 m
  3. 31.6 m
  4. 42.2 m
  5. 59.4 m
  6. 67.2 m
Answer.
F.

Calculation 7.15.6. Wave Intensity.

Consider a logarithmic function like that found in the equation for decibels (also used for the Richter scale, by the way). If the sound intensity level increases from 30 dB to 60 dB, what can you say about the intensity of the wave?
  1. The intensity must have decreased by a factor greater than 2
  2. The intensity must have decreased by a factor of 2
  3. The intensity must have decreased by a factor less than 2
  4. The intensity must have remained constant
  5. The intensity must have increased by a factor greater than 2
  6. The intensity must have increased by a factor of 2
  7. The intensity must have increased by a factor less than 2
Answer.
E.

Calculation 7.15.7. Sound Intensity.

If the sound intensity level at a certain point increases from \(30 \mathrm{~dB}\) to \(60 \mathrm{~dB}\text{,}\) by what factor did the intensity change?
  1. 0.5
  2. 2
  3. 30
  4. 100
  5. 1000
Answer.
E.

Calculation 7.15.8. Sound at a Concert.

You are attending a concert by your favorite band, but you can barely hear them, because only 2 of the 20 speakers are working. The sound intensity level at your location is \(60 \mathrm{~dB}\text{.}\) If all 20 speakers suddenly start working, what is the new sound intensity level at your location? Assume that you don’t change your location and that all of the speakers are the same distance from you.
  1. 70 dB
  2. 78 dB
  3. 100 dB
  4. 120 dB
  5. 600 dB
Answer.
A.

Calculation 7.15.9. Ambulance Siren.

You hear the siren from an ambulance and the frequency you hear is decreasing. Which of the following can you conclude are plausible?
  1. The car is receding from you at a constant speed.
  2. The car is receding from you at an increasing speed.
  3. The car is receding from you at a decreasing speed.
  4. The car is approaching you at a constant speed.
  5. The car is approaching you at an increasing speed.
  6. The car is approaching you at a decreasing speed.
Answer.
B., F.

Calculation 7.15.10. Dolphin Frequency.

Dolphins emit clicks of sound for communicating and echo-location. A marine biologist, standing at rest in shallow seawater, is monitoring a dolphin swimming directly away at 8 m/s. The biologist measures the number of clicks occurring per second to be at a frequency of 2500 Hz. The speed of sound in calm seawater is 1522 m/s. What is the frequency of the clicks that the dolphin sends out?
  1. 1522 Hz
  2. 2464 Hz
  3. 2487 Hz
  4. 2500 Hz
  5. 2513 Hz
  6. 2536 Hz
Answer.
E.

Calculation 7.15.11. Tube of Air.

A cylindrical tube of air sustains standing waves at 600 Hz, 800 Hz, and 1000 Hz, but at no other frequencies between 600 and 1000 Hz. Which of the following statements are plausible here?
  1. The fundamental frequency is 50 Hz and the tube is open on both ends.
  2. The fundamental frequency is 100 Hz and the tube is open on both ends.
  3. The fundamental frequency is 100 Hz and the tube has one open and one closed end.
  4. The fundamental frequency is 200 Hz and the tube has one open and one closed end.
  5. The fundamental frequency is 200 Hz and the tube is open on both ends.
  6. The fundamental frequency is 200 Hz and the tube is closed on both ends.
Answer.
E., F.

Calculation 7.15.12. Speakers.

Suppose you observe that the shortest non-zero path length difference that produces constructive interference from two coherent unknown sources is \(128 \mathrm{~m}\text{.}\) What is the wavelength of the source?
At which of the following path length differences will constructive interference also occur?
  1. 64 m
  2. 180 m
  3. 256 m
  4. 320 m
  5. 512 m
  6. 832 m
  7. 3264 m
  8. 4096 m
At which of the following path length differences will destructive interference occur?
  1. 64 m
  2. 180 m
  3. 256 m
  4. 320 m
  5. 512 m
  6. 832 m
  7. 3264 m
  8. 4096 m
Answer 1.
\(128 \mathrm{~m}\)
Answer 2.
C., E., H.
Answer 3.
A., D., F., G.

Subsection Study

A*R*C*S 7.15.13. Jet Engine.

During takeoff, the sound intensity level of a jet engine is \(150 \mathrm{~dB}\) at a distance of \(22 \mathrm{~m}\text{.}\) What is the sound intensity level at a distance of \(1.0 \mathrm{~km}\text{?}\)

A*R*C*S 7.15.14. Wave Amplitude.

A sinusoidal wave travels along a stretched string. A particle on the string has a maximum velocity of \(1.40 \mathrm{~m/s}\) and a maximum acceleration of \(270 \mathrm{~m/s^2}\text{.}\) Find the frequency and amplitude of the wave.

A*R*C*S 7.15.15. Silent Speakers.

Two speakers separated by \(10 \mathrm{~m}\) are simultaneously creating identical (with the same initial phase) sound waves with wavelength \(8 \mathrm{~m}\text{.}\) You are standing somewhere on the line in between the two speakers, but you do not hear any sound! Determine where you are standing, measured from the center point between the two speakers.

Subsection Apply

Explanation 7.15.16. Reflecting Waves.

The diagram below shows a wave pulse at \(t = 0\) moving to the right on a string with wave speed \(2 \mathrm{~mm/s}\text{.}\) Each grid box represents \(1 \mathrm{~mm}\text{.}\) Consider two different scenarios:
  • In Scenario 1 the black dot represents a fixed end for the string
  • In Scenario 2 the black dot represents an end that is free to move up and down
For each scenario: Sketch the shape of the spring at \(t_1 = 2 \mathrm{~s}\text{,}\) \(t_2 = 2.5 \mathrm{~s}\text{,}\) and \(t_3 = 3 \mathrm{~s}\text{.}\) Explain how you made your sketches and comment on the similarities and differences between the scenarios.
Figure 7.15.1.
A wave pulse moving to the right.

Explanation 7.15.17. Wave at a Boundary.

Two strings are tied together and a wave is sent down string 1. String 1 has a linear mass density three times smaller than string 2. When the wave reaches the point where the strings are tied together and moves through string 2, you observe the wavelength. Is the wavelength in string 2 greater than, less than, or equal to the wavelength in string 1?

A*R*C*S 7.15.18. Diving Bird.

You hear a loud noise at \(900 \mathrm{~Hz}\) and look up to see a bird diving toward you. You are able to identify the type of bird and you know that they usually make noise at around \(800 \mathrm{~Hz}\text{.}\) How fast is the bird moving?

A*R*C*S 7.15.19. Flash of Lightning.

You see a flash of lightning strike a clock tower during a thunderstorm. You count \(2.5 \mathrm{~s}\) between when the lightning flashes and when you hear thunder with a sound level of \(70 \mathrm{~dB}\text{.}\) What is the sound level of the thunder for someone standing only \(20 \mathrm{~m}\) from the clock tower?

References References

[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
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