LECTURE 6 WAVES

Instructor: Kazumi Tolich Lecture 6

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¨ Reading chapter 14.4 to 14.5 ¤ ¤ Frequency of a sound wave ¤ Sound intensity ¤ Intensity level & human perception of sound Quiz: 1

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¨ Does a longitudinal wave, such as a sound wave, have an amplitude? A. yes B. no C. it depends on the medium the wave is in Quiz: 6-1 answer

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¨ Yes

¨ Both transverse and longitudinal waves have all of these properties: ¤ wavelength ¤ frequency ¤ amplitude ¤ velocity ¤ period Sound waves/Demo: 1

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¨ Sound waves are carried by oscillating molecules in air (or other medium carrying the sound), causing the density and pressure of the air to oscillate.

¨ The speed of sound is different in different materials; in general, the denser the material, the faster sound travels through it.

¨ In this class, we will use the speed of sound in air to be 343 m/s.

¨ Demo: Siren in Vacuum Quiz: 2

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¨ When a sound wave passes from air into water, what properties of the wave will change? Choose all that apply. A. The frequency B. The wavelength C. The speed of the wave Quiz: 6-2 answer

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A. The frequency

B. The wavelength

C. The speed of the wave

¨ Wave speed must change (different medium).

¨ Frequency does not change (determined by the source).

¨ Now, � = �� and because � has changed and � is constant then � must also change. Frequency of a sound wave/Demo: 2

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¨ The frequency of a sound wave is its pitch.

¨ Sound waves can have any frequency; the human ear can hear between about 20 Hz and 20,000 Hz.

¨ Sounds with frequencies greater than 20,000 Hz are called ultrasonic; sounds with frequencies less than 20 Hz are called infrasonic.

¨ Speed of sound in air is independent of its frequency. Quiz: 3

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¨ If you fill your lungs with helium and then try talking, your voice sounds high-pitched. Assume that the wavelength of the sound wave of your voice remains constant as it is determined by the length of the vocal chords. What conclusion can you reach about the speed of sound in helium? A. Speed of sound is less in helium B. Speed of sound is the same in helium C. Speed of sound is greater in helium D. This effect has nothing to do with the speed in helium. Quiz: 6-3 answer

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¨ Speed of sound is greater in helium ¨ The higher pitch implies a higher frequency.

¨ Because � = ��, and � remains constant, the speed of the wave has increased. Intensity

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¨ Intensity is the amount of energy, �, that passes through a given area, �, in a given time, �, or power, �, over the area.

� � � = = �� �

¨ The energy from a point source is distributed uniformly over a spherical surface of radius �.

� � = 4�� Quiz: 4

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¨ You hear a fire truck with a certain intensity, and you are about 1 mile away. Another person hears the same fire truck with an intensity that is about 10 times less. How far is the other person from the fire truck in miles? Quiz: 6-4 answer

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¨ 3.2 miles ¨ Assuming that the fire truck is a point source, the intensity drops as � = . ¨ = = = 10 ¨ � = 10� = 3.2 miles

1 2 Intensity level and loudness/Demo: 3

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¨ Our perception of loudness is given by intensity level, � in :

� � = 10 dB log �

¤ � is the the threshold of hearing, or faintest sound that can be heard, 10-12 W/m2. ¤ The sensation of loudness depends on the frequency as well as the intensity of a sound. Human ears are most sensitive at ~4kHz. ¨ Decibel meter demo Quiz: 5

¨ When his radio breaks, Chuck purchases a new one that produces twice as much acoustic power as the old one. His expectation is that his new radio will sound twice as loud as his old radio. Will he be disappointed? A. Yes, he will be disappointed, the new radio will sound less than twice as loud. B. No, he won’t be disappointed, the new radio will sound twice as loud. C. No, he won’t be disappointed, in fact the new radio will sound more than twice as loud. Quiz: 6-5 answer

¨ Yes, he will be disappointed, the new radio will sound less than twice as loud.

¨ Our perception of loudness varies logarithmically with intensity.

¨ Since the new radio produces twice as much acoustic power as the old one,

where βold is probably around 80 dB to 90 dB. Quiz: 6

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¨ What is the intensity for the threshold of pain in W⁄m? Quiz: 6-6 answer

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2 ¨ 1 W/m

¨ The threshold of pain for intensity level is 120 dB. ¨ 120 dB = 10 dB log ¨ 12 = log ¨ 10 = ¨ � = 10 � = 10 10 W⁄m = 1 W⁄m Example 1

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¨ A salesperson claimed that a stereo system with several speakers has a maximum of P = 120 W. Organizing the speakers to simulate a point source, you could get as close as r = 1.2 m with the volume full on before the sound hurt your ears. Should you report the firm to the Consumer Product Safety Commission?