Question

A longitudinal wave propagating in a water-filled pipe has intensity $3.00\times {10}^{-6}\frac{w}{m^2}$ and frequency 3400 Hz. Water has density $1000\frac{kg}{m^3}$ and bulk modulus $2.18\times {10}^9$ Pa. If the pipe is then filled with air at pressure $1.00\times {10}^5$ Pa and density $1.20\frac{kg}{m^3}$, and the a wave with the same intensity and frequency is propagated, What is the ratio of the two amplitudes in both media?

• A. 4
• B. 2.25
• C. 1.75
• D. None of these

Answer 1

The correct option is B

2.25

$I=2{\pi }^2{A}^2{f}^{2}pV$

$\frac{Forwater}{3.00\times {10}^{-6}}=2{\pi }^2\times A^2\times (3400{)}^2\times v$

$v=\sqrt{\frac{B}{p}}=\sqrt{\frac{2.18\times {10}^9}{1000}}$

$A^2=\frac{3.00\times {10}^{-6}\times \sqrt{1000}}{2{\pi }^2\times (3400{)}^2\times \sqrt{2.18\times {10}^9}}$

$A_{\omega }=2.99\times {10}^{-9}m$

$\stackrel{\sim }{\sim }3nm$

For air

$3.00\times {10}^{-6}=2{\pi }^2\times A^2\times (3400{)}^2\times \sqrt{\frac{{10}^5}{1.2}}$

$A_{\omega }=6.75\times {10}^{-9}m$

Now $\frac{A_a}{A_{\omega }}=\frac{6.75}{3}=2.25$