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 344 m/s through air with a uniform density of 1.41 kg/m^3. The vertical axis scale is set by Delta p_s = 4.20 mPa. If the displacement function of the wave is written as s(x, t) = s_m cos(kx - omega t), what are s_m, k, and omega? The air is then cooled so that its density is 1.35 kg/m^3 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 s_m, k, and omega?

Explanation / Answer

a) From Graph

T=2.30 ms and

dPm=4.2*2.30 =9.66 mpa

W=2pi/T =2pi/(2.30*10-3)=2730.4 rad/s

The Change in Pressure

dPm=v*p*W*Sm

(9.66*10-3)=344*1.41*2730.4*Sm

Sm=7.29*10-9 m

b)

K=W/v =2730.4/344

K=7.93 N/m

c)

W=2730.4 rad/s

d)

The Change in Pressure

dPm=v*p*W*Sm

(9.66*10-3)=323*1.35*2730.4*Sm

Sm=8.11*10-9 m

e)

K=W/v =2730.4/323

K=8.45 N/m

f)

W=2730.4 rad/s

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