# lec3 - Sound Waves Ken Intriligators week 3 lectures Ken...

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Sound Waves Ken Intriligator’s week 3 lectures, Oct 14, 2013 Ken: “OK,let’s get started..” Monday, October 14, 2013

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Sound = pressure wave s ( x, t ) displacement fluctuation satisfies 3d wave equation: s ( x, t ) ( 2 - 1 v 2 2 t 2 ) s ( x, t ) = 0 2 f ( r ) = 1 r 2 r 2 ( rf ( r )) r = spherical, radial coordinate 2 = 2 x 2 + 2 y 2 + 2 z 2 Monday, October 14, 2013
3d wave eqn. solutions s ( x, t ) = A cos( k · x - ω t + φ ) “Plane wave” unit vector point in dir. of wave velocity k = kn k = 2 π λ n = ω = vk “Spherical wave” s ( r, t ) = A r cos( kr - ω t + φ ) ω = vk Consider first plane waves, in the x direction: s ( x, t ) = A cos( kx - ω t + φ ) Monday, October 14, 2013

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Derive the wave eqn.: p ( x, t ) = gauge pressure p tot = p 0 + p p = - B ( dV/V ) B= “bulk modulus,” it’s just like the spring constant k in F = -kx. F/V = ( m/V ) a - p x = B 2 s x 2 = ρ 0 2 s t 2 v sound = B ρ 0 Fits with D.A.! p = - B s x (“Incompressible” fluid has B=infinity) 2 s x 2 = 1 v 2 2 s t 2 dx A Monday, October 14, 2013
Examples v sound = B ρ 0 Water: ρ 0 = 10 3 kg/m 3 B = 2 . 18 × 10 9 Pa v sound 1480 m/s v sound 344 m/s Air: v gas = γ kT m We’ll understand gasses later. For this week, ignore all parts of the chapter mentioning temperature T. Ignore this now, for later. Monday, October 14, 2013

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Ear’s f (freq) ranges v sound 344 m/s v sound = λ /T = λ f 20 Hz f 20 , 000 Hz 1 . 7 cm λ 17 . 5 m Humans: Dogs: 40 Hz f 60 , 000 Hz Cats: 60
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