(a) If two sound waves, one in a gas medium and one in a liquid medium, are equa

Question

(a) If two sound waves, one in a gas medium and one in a liquid medium, are equal in intensity, what is the ratio of the pressure amplitude of the wave in the liquid to that of the wave in the gas? Assume that the density of the gas is 1.76 kg/m3 and the density of the liquid is 1230 kg/m3. The speed of sound is 348 m/s in the gas medium and 1020 m/s in the liquid. (b) If the pressure amplitudes are equal instead, what is the ratio of the intensities of the waves (of the one in the liquid to that in the gas)?

Explanation / Answer

(a)

the intensity of a sound wave is given by

I =p2/(2dv)

p - presuure amplitude of the wave

d - density of the medium

v - velocity of sound in the medium

p12 /(2d1*v1) = p22/(2d2*v2)

p12 /p22 = (2d1*v1)/(2d2*v2)

=d1*v1 /d2*v2

   = 1.76*348/1230*1020

= 0.000488

p1/p2 = 0.022

where 1- gas

2- liquid

Pliq /Pgas = 1/0.022

= 45.45

(b)

now pressure amplitudes are equal so

I1d1v1 = I2d2v2

I2/I1 = d1v1/d2v2

= 0.00048

Iliq/Igas = 0.00048

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