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Question

(a) A longitudinal wave propagating in a water-filled pipe has intensity 3.00×106W/m2 and frequency 3400 Hz. Find the amplitude A and wavelength λ of the wave. Water has density 1000kg/m3 and bulk modulus 2.18×109 Pa.

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Solution

Given- K=2.18×109Pa,I=3.00×106W/m2,f=3400Hz,ρ=1000kg/m3, ,
speed of sound in a medium is given by ,
v=(K/ρ) ,
v=(2.18×109/1000)=1.48×103m/s ,
we have , v=fλ ,
or λ=v/f=1.48×103/3400=0.43m ,
now intensity of longitudinal wave is given by ,
I=2π2f2A2vρ ,
or A2=I/(2π2f2vρ)=3.00×1062×3.142×34002×1.48×103×1000=8.89×1021m ,
or A=9.43×1011m

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