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

Answer: 1

$P=\frac{1}{2}\rho {\omega }^2{A}^{2}sV$
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 $P_0=B_{0}Ak$
${\left(P_0\right)}_1/{\left(P_0\right)}_2=\left(\frac{A_1}{A_2}\right)\left(\frac{k_1}{k_2}\right)$
$=\left(\frac{A_1}{A_2}\right)\left(\frac{{\lambda }_2}{{\lambda }_1}\right)=\left(\frac{1}{2}\right)\left(\frac{2}{1}\right)=1$