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Sound

Sound. Physics 202 Professor Lee Carkner Lecture 8. Sound. More generally: sound = longitudinal wave Unlike waves on a string, a sound wave propagates outward in all 3 dimensions Example: String wave 1D, sound wave 3D. Sound Speed. For sound the velocity is: v = (B/ r ) ½

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Sound

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  1. Sound Physics 202 Professor Lee Carkner Lecture 8

  2. Sound • More generally: sound = longitudinal wave • Unlike waves on a string, a sound wave propagates outward in all 3 dimensions • Example: • String wave 1D, sound wave 3D

  3. Sound Speed • For sound the velocity is: v = (B/r)½ • Bulk modulus is like tension (how “springy” the fluid is) • Density is like linear density B = - Dp/(DV/V) • Example: Water is more dense than air, so why does sound travel faster in water? • It has a much larger B. Water is hard to compress

  4. Wave Equations • The displacement of any element of air will also be in the x direction and is represented by: s(x,t) = sm cos (kx-wt) • This is similar to the transverse wave equation but does not involve y

  5. Pressure Wave

  6. Pressure Dp(x,t) = Dpm sin (kx - wt) • Where Dpm is the pressure amplitude Dpm = (vrw) sm • This is not an absolute pressure but rather a pressure change

  7. Pressure Wave Equation

  8. Pressure and Displacement • The pressure and the displacement variations are p/2 radians out of phase • When the displacement is zero the pressure is a maximum • and away from where pressure is low

  9. Interference • If an observer is an equal distance from each, the sound will be in phase • For a phase difference of 2p the path length difference is l f/2p = DL/l f = 2p (DL/l)

  10. Constructive and Destructive DL=ml • The sound will be at max amplitude (louder than an individual source) DL = (m+½)l • You can also have intermediate interference making the sound louder or softer

  11. Interference and You • Why don’t we notice interference much? • Each with a different DL • You hear a combination of many different L • Not all will have strong interference at your location • You don’t hold perfectly still at the spot with maximum interference

  12. Intensity of Sound I = P/A • The units of intensity are W/m2 I = ½rvw2sm2 • Compare to expression for power in a transverse wave • Depends on the square of the amplitude and the frequency (wave properties)

  13. Intensity and Distance • As you get further away from the source the intensity decreases because the area over which the power is distributed increases I = P/A = Ps/(4pr2) • Sounds get fainter as you get further away because the energy is spread out over a larger area • I falls off as 1/r2 (inverse square law)

  14. Inverse Square Law Source r A1=4pr2 I1 = Ps/A1 2r A2=4p(2r)2 = 16pr2 = 4A1 I2 = Ps/A2 = ¼ I1

  15. Next Time • Read: 17.5-17.10

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