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.

A $0.900 \mathrm{m}$ long tube is closed at one end. A stretched wire is placed near the open end. The wire is $0.330 \mathrm{m}$ long and has a mass $9.60 \mathrm{g}$. It is fixed at both the ends and oscillated in its fundamental mode. By resonance, it sets the air column in the tube to oscillation at that column's second lowest harmonic frequency.(Take, velocity of sound as $330 \mathrm{m} {\mathrm{s}}^{-1}$)

Find

$\left(A\right)$ that frequency.

$\left(B\right)$ the tension in the wire.

$\left(A\right)$ Find the speed of waves on a violin string of mass $860 \mathrm{mg}$ and length $22.0 \mathrm{cm}$ when the fundamental frequency is $920 \mathrm{Hz}$.

$\left(B\right)$ What is the tension in the string?

For the fundamental, what is the wavelength of,

$\left(C\right)$ the waves on the string?

$\left(D\right)$ the sound waves emitted by the string?

(Take, velocity of sound in air as $343 \mathrm{m} {\mathrm{s}}^{-1}$)

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) $\lambda$?