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Sound is a longitudinal pressure wave that can travel through many substances, though humans normally hear it through air. The human sense of hearing responds to sound waves with frequencies that range from about 20 Hz up to 20,000 Hz. High frequencies are perceived as high pitch and large-amplitude sound waves are perceived as loud. The amplitude of a sound wave is measured using the logarithmic decibel scale: An increase of 20 dB means that the amplitude of a sound wave has been multiplied by a factor of 10. The Doppler effect describes how a sound wave’s pitch is altered when its source moves toward or away from the listener. Supersonic (faster-than-sound) motion through a substance creates a shock wave in that substance. 
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pitch, speed of sound, decibel (dB), supersonic, Doppler effect
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Review problems and questions |
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- These three graphs show the relative amplitudes of three different sound waves, each as a function of time.
- Which of the three sound waves has the lowest pitch?
- Is that pitch high enough for the typical human to hear?
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Answer: - Sound B has the lowest pitch.
- Yes; Sound B can be heard by humans.
Solution: - Sound B has the lowest pitch. Pitch is proportional to frequency: A higher frequency indicates a higher pitch. In contrast, frequency is lowest when period is longest (since they are inversely proportional to one another). The wave with the longest period is the one that repeats itself after the longest amount of time. The periods of the three wave patterns, in seconds, are TA = 0.02, TB = 0.04, and TC = 0.025, respectively. Sound B has the longest period and, therefore, the lowest pitch.
- Yes; Sound B can be heard by humans. The frequency of Sound B is fB = 1/TB = 25 Hz, and this is higher than 20 Hz, the lowest frequency audible to the typical human.
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- One valuable assistive technology is the hearing aid, an electronic device that contains a small amplifier to boost sound strength.
- Suppose that one hearing aid multiplies the amplitude of sound waves by a factor of 10. How many decibels will the hearing aid add to the sounds it detects?
- Another hearing aid adds 40 dB to the sounds it detects. By what factor does it multiply sound amplitude?
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Answer: - This hearing aid adds 20 dB to the sounds it picks up.
- This hearing aid multiplies the amplitudes of sound waves by a factor of 100.
Solution: - This hearing aid adds 20 dB to the sounds it picks up. Recall the definition of the decibel: adding 20 dB to a sound is equivalent to multiplying sound-wave amplitude by a factor of 10. (This puzzling mathematical behavior is an example of a logarithmic function. Many human perceptions, such as of star brightnesses, are logarithmic in nature.)
- This hearing aid multiplies the amplitudes of sound waves by a factor of 100. Adding 40 dB is the same as adding 20 dB twice. In turn, that is the same as multiplying amplitude by 10 and then multiplying it by 10 once more. A 40 dB hearing aid would assist people with fairly severe limitations, but it would require a safety feature: Sounds that already were loud would have to be amplified much less (or not at all). Otherwise, the user’s hearing could be damaged even further.
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- Return to the graphs near the top of this page. Suppose that Sound A and Sound B both came from the same source and had the same original frequency f0. Now consider that one of the sounds was heard as the source approached you, while the other was heard after the source passed you and receded into the distance.
- Which sound (A or B) was from the source when approaching?
- The source was moving at a speed of 114 m/s. What was the source’s actual sound frequency, f0? (Assume a sound speed vs of 343 m/s.)
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Answer: - Sound A came from the approaching source.
- The actual emitted sound frequency is f0 = 33.3 Hz.
Solution: - Sound A came from the approaching source. The Doppler effect increases the frequency when a sound source approaches the listener. Sound A has a shorter period, and hence a higher frequency, than Sound B; therefore, Sound A came from the approaching source.
- The actual emitted sound frequency is f0 = 33.3 Hz. This frequency can be calculated by using either the frequency of Sound A or of Sound B. The solution below uses Sound A, which has an observed frequency of (6 cycles)/(0.12 s) = 50 Hz as heard when the source approaches at 114 m/s. Rearranging gives
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