A point source emits sound waves isotropically. The intensity of the waves $6.00 \mathrm{m}$ from the source is $4.5\times {10}^{-4}\mathrm{W} {\mathrm{m}}^{-2}$. Assuming that the energy of the waves is conserved, find the power of the source.

Show the output from a pressure monitor mounted at a point along the path taken by a sound wave of a single frequency traveling at $343 \mathrm{m} {\mathrm{s}}^{-1}$ through air with a uniform density $1.21 \mathrm{kg} {\mathrm{m}}^{-3}$. The vertical axis scale is set by $∆p_{\mathrm{s}}=5.0 \mathrm{mPa}$.The displacement function of the wave is $s\left(x,t\right)=s_{\mathrm{m}}\hspace{0.17em}\cos \left(kx-\mathrm{\omega }t\right)$.

What is

$\left(A\right)$ $s_{\mathrm{m}}$?

$\left(B\right)$ $\mathrm{k}$?

$\left(C\right)$ $\mathrm{\omega }$?

The air is then cooled so that its density is $1.35 \mathrm{kg} {\mathrm{m}}^{-3}$ and the speed of a sound wave through it is $320 \mathrm{m} {\mathrm{s}}^{-1}$. The sound source again emits the sound wave at the same frequency and same pressure amplitude.

What is

$\left(D\right)$ $s_{\mathrm{m}}$?

$\left(E\right)$ $\mathrm{k}$?

$\left(F\right)$ $\mathrm{\omega }$?

A violin string $15.0 \mathrm{cm}$ long, fixed at both ends oscillates in $n=1$ mode. The speed of waves on the string is $280 \mathrm{m} {\mathrm{s}}^{-1}$, and the speed of sound in air is $348 \mathrm{m} {\mathrm{s}}^{-1}$.

What is the

$\left(A\right)$ frequency of the emitted sound wave?

$\left(B\right)$ wavelength of the emitted sound wave?

Figure shows four isotropic point sources of sound that are uniformly spaced on the $x$-axis. The sources emits sound at the same wavelength $\lambda$ and same amplitude $S_{\mathrm{m}}$, and they emit in phase. A point $P$ is shown on the $x$-axis. Assume that as the sound waves travel to $P$, the decrease in their amplitude is negligible. What multiple of $S_{\mathrm{m}}$ is the amplitude of the net wave at $P$, if the distance $d$ in the figure is (a) $\frac{\lambda }{4}$, (b) $\frac{\lambda }{2}$ and (c) $\lambda$?

In French submarine and a U.S. Submarine move towards each other during maneuvers in motionless water in the North Atlantic. The French sub moves at the speed, $V_{\text{F}}=48.00\mathrm{km} {\mathrm{h}}^{-1}$ and the U.S. sub at $V_{\text{US}}=72.00\mathrm{km} {\mathrm{h}}^{-1}$. The French sub sends out a sonar signal (sound wave in water) at $1.560\times {10}^3\mathrm{Hz}$. Sonar waves travel at $5470 \mathrm{km} {\mathrm{h}}^{-1}$. (a) What is the signal's frequency as detected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub?