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/m^3. The vertical axis scale is set by delta rho_s = 4.40 mPa. If the displacement function of the wave is written as s(x, t) = s_m cos(kx - omega t), what are (a) s_m, (b) k, and (c) omega? The air is then cooled so that its density is 1.85 kg/m^3 and the speed of a sound wave through it is 322 m/s. The sound source again emits the sound wave at the same frequency and same pressure amplitude. What now are (d) s_m, (e) k, and (f) omega?

Explanation / Answer

a) From Graph

T=2.00 ms and

dPm=4.4*2.00 =8.80 mpa

W=2pi/T =2pi/(2.00*10-3)=3141.6 rad/s

The Change in Pressure

dPm=v*p*W*Sm

(8.80*10-3)=343*1.41*3141.6*Sm

Sm=5.79*10-9 m

b)

K=W/v =3141.6/343

K=9.16 N/m

c)

W=3141.6 rad/s

d)

The Change in Pressure

dPm=v*p*W*Sm

(8.80*10-3)=322*1.85*3141.6 *Sm

Sm=4.70*10-9 m

e)

K=W/v =3141.6/322

K=9.76 N/m

f)

W=3141.6 rad/s

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