Question

The average power transmitted across a cross-section by two sound waves moving in the same direction are equal. The wave lengths of two sound waves are in the ratio of $1: 2$, then the ratio of their pressure amplitudes is______

Answer 1

$P=\frac{1}{2} \rho \omega^{2} A^{2} s V$
Since $\frac{\lambda_{1}}{\lambda}=\frac{1}{2}, \frac{f_{1}}{f_{2}}=\frac{\omega_{1}}{\omega_{2}}=\frac{2}{1}$
Since $P_{1}=P_{2}, \omega_{1} A_{1}=\omega_{2} A_{2}, \frac{A_{1}}{A_{2}}=\frac{\omega_{2}}{\omega_{1}}=\frac{1}{2}$
Pressure amplitude $P_{0}=B_{0} A k$
$\left(P_{0}\right)_{1} /\left(P_{0}\right)_{2}=\left(\frac{A_{1}}{A_{2}}\right)\left(\frac{k_{1}}{k_{2}}\right)$
$=\left(\frac{A_{1}}{A_{2}}\right)\left(\frac{\lambda_{2}}{\lambda_{1}}\right)=\left(\frac{1}{2}\right)\left(\frac{2}{1}\right)=1$