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Chapter 20

Chapter 20. Sound and Hearing. Wavelength ( ). Period (T ). y. y. A. A mplitude. t. x. Sound: A longitudinal wave in a medium. Sound can travel in air, gas, liquid and solid.

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Chapter 20

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  1. Chapter 20 Sound and Hearing

  2. Wavelength () Period (T) y y A Amplitude t x Sound: A longitudinal wave in a medium. Sound can travel in air, gas, liquid and solid. Sound waves can be represented by sinusoidal waves with definite frequency (f), wavelength () and amplitude (A).

  3. Audible range is from 20 to 20,000 Hz (in octave or 1/3 octave band). The speaking voice frequencies are about 145 Hz in men and about 230 Hz in women in the average. Ultrasonic: sound with higher frequency (above the audible range) Infrasonic: sound with lower frequency (below the audible range) In general, the stiffer the medium, the faster the sound transmitted. i.e. speed of sound in solids is the greatest and that in gas is lowest. E.g. 343 m/s in air (20oC), 1498 m/s in water, 5000 m/s in steel. The speed of sound also depends on temperature, and is most significant for gaseous medium. e.g. sound in air v  (331 + 0.60 T) m/s where T is in C Human has two subjective sensations on sound. The pitch of sound is determined by its frequency and loudness is related to the energy. However, pitch is influenced by the loudness of the sound: increase in sound intensity decreases the pitch for low frequencies and increases it for high ones.

  4. Sound Pressure Level (SPL) and where Prms = pressure amplitude (Pa or N/m2) P0 = reference pressure amplitude 2x10-5 Pa

  5. Sound Intensity Level (SIL) Loudness or intensity of a sound decreases as an observer gets farther from the source of the sound. and where  = density of medium, kg/m3 c = velocity of sound in the medium, m/s R = distance from the source Human ear can detect a large range of sound intensity from 10-12 W/m2 to 1W/m2. The intensity level LI in decibels is defined to be ten times the logarithm of the ratio of two intensities I and Io: where Io = reference intensity (1x10-12 W/m2).

  6. Sound Power Level (SWL)  where W0 = reference sound power (1x10-12 Watt) Example 20.1 In a party, a stereo tape deck is playing at maximum volume. Suddenly a dancer trips over a wire, and one speaker stops playing. What is the reduction in sound intensity level, measured in dB? (Assume equal sound level is produced by each speaker) Solution: When one speaker fails, the resulting sound intensity is one-half of the initial intensity, therefore, Ifinal = 0.5 Io

  7. Example 20.2 What are the intensity levels for sounds with intensities of (a) 10-12 W/m2 and (b) 5.0 x 10-6 W/m2? (Given the intensity of threshold of hearing = 10-12 W/m2) Solution: (a) (b) Example 20.3 An engine-powered lawnmower is rated at 95 dB. (a) What is the sound intensity for this particular mower? (b) How many times more intense is the sound of this mower than that of an electric-powered mower rated at 83 dB? (c) If this machine is operated in a room with background sound intensity level at 70 dB, what will be the measured sound intensity level? Solution:

  8. (c) Only intensity can be added, not sound intensity level Ia = 3.2  10-3 W/m2 from part (a) IBackground= Io 1070/10 = 1  10-5 W/m2 Ia + IBackground = 3.2 x 10-3 W/m2 + 1  10-5 W/m2 = 321  10-5 W/m2 i.e. no change (as 70 dB has intensity 2 order less than 95 dB)

  9. Doppler EffectWhen the source of wave is moving towards an observer, the pitch (frequency) is higher than when the source is at rest; and when the source is travelling away from the observer, the pitch (frequency) is lower. This phenomenon is known as the Doppler effect. (1) Source is moving

  10. During one period T of the source, the wave moves out a distance vT and the source moves a distance vsT. Therefore, the wavelength observed by O is o: o = (v - vs) T = (v - vs) / f The observed frequency fo = v / o (2) Observer is moving

  11. (3) Source and observer both moving ** vs = +ve if the source is moving towards the observer. vo = +ve if the observer is moving away from the source. Example 20.4 A 5000 Hz sound wave is directed toward an object moving 3.5 m/s toward the (stationary) source. What is the frequency of the reflected wave? (assume sound velocity = 343 m/s) Solution There are actually two Doppler shifts in this situation. First, the object acts like a moving observer and “detects” a sound wave of frequency fo: vo = -3.5 m/s, vs = 0, v = 343 m/s The object then acts like a moving source remitting (reflecting) the sound, so the reflected frequency is fo’: vo = 0, vs = +3.5 m/s

  12. Beats If two sources of sound of similar frequency are sounded together, a phenomenon known as beats occurs. The combined effect of the two sources gives an alternately rises and falls of sound level as shown below. The rate at which the loudness maxima occur is the beat frequency, which is equal to the difference of the two sound frequencies. i.e. fb = f1 – f2 Example 20.5 A 5000 Hz sound wave is directed toward an object moving 3.5 m/s toward the (stationary) source. How many beats per second will be heard at the sound source? (assume sound velocity = 343 m/s) Solution From the above example, fb = 5103 –5000 =103 Hz

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