The figure shows the output from a pressure monitor mounted at a point along the

Question

The figure shows the output from a pressure monitor mounted at a point along the path taken by a sound wave of a single frequency traveling at 343 m/s through air with a uniform density of 1.41 kg/m3. The vertical axis scale is set by ps = 4.10 mPa. If the displacement function of the wave is written as s(x, t) = sm cos(kx - t), what are (a) sm, (b) k, and (c) ? The air is then cooled so that its density is 2.05 kg/m3 and the speed of a sound wave through it is 323 m/s. The sound source again emits the sound wave at the same frequency and same pressure amplitude. What now are (d) sm, (e) k, and (f) ?

Explanation / Answer

part C = W = 2pi f = 2pi/T

W = 2*3.14/(2.2 e -3)

W = 2.85 e 3 rad/s

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part B :

as V = W/k

K = W/v = 2..85 e 3/(343) = 8.31 per m

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[part A :

W = sqrt(B/sm)

B = V^2 rho

B = 343*343* 1.21 = 1.42 e 5

noew use rho s = B k Sm

4.1 e -3 /(1.42 e 5 * 8.31 * sm

Sm = 34 A0

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