Embibe Experts Solutions for Chapter: Sound Waves, Exercise 4: Exercise-4

The displacement sound wave in a medium is given by the equation $Y=A\cos (ax+bt)$ where $A, a$ and $b$ are positive constants. The wave is reflected by a denser obstacle situated at $x=0.$ The intensity of the reflected wave is $0.64$ times that of the incident wave. Tick the statement among the following that is incorrect.

A cylindrical tube, open at one end and closed at the other is in acoustic unison (resonance) with an external source of sound of single frequency held at the open end of the tube in its fundamental note. Then,

Two narrow organ pipes, one open (length $L_1$) and the other closed (length $L_2$) are sounded in their respective fundamental modes. The beat frequency heard is $5 \mathrm{Hz}$. If now the pipes are sounded in their first overtones, then also the beat frequency heard is $5 \mathrm{Hz}$. Then:

The effect of making a hole exactly at $(1/3^{\mathrm{rd}})$ of the length of the pipe from its closed end is such that

In a resonance tube experiment, a closed organ pipe of length $120 \mathrm{cm}$ is used. Initially it is completely filled with water. It is vibrated with tuning fork of frequency $340 \mathrm{Hz}.$ To achieve resonance, the water level is lowered then (given $v_{\mathrm{air}}=340 \mathrm{m} {\mathrm{s}}^{-1},$neglect end correction):

Two sound waves one in air and the other in freshwater are equal in intensity.
$\left(a\right)$ Find the ratio of pressure amplitudes of the wave in water to that of the wave in air.

$\left(b\right)$ If the pressure amplitudes of the waves are equal in then what will be the ratio of the intensities of the waves.
$\left[v_{\mathrm{sound}}=340 \mathrm{m} {\mathrm{s}}^{-1}\right.$in air $\&$ density of air $=1.22 \mathrm{kg} {\mathrm{m}}^{-3}, v_{\mathrm{sound}}=1488 \mathrm{m} {\mathrm{s}}^{-1}$ in water]

If the number of possible natural oscillations of the air column in a pipe whose frequencies lie below $v_0=$$1250 \mathrm{Hz}.$ The length of the pipe is $L=85 \mathrm{cm}$. The velocity of sound is  $340 \mathrm{m} {\mathrm{s}}^{-1}$.
$\left(a\right)$ When the pipe is closed from one end is $n_1$

$\left(b\right)$ When the pipe is opened from both ends is $n_2$.

Then find the value of $n_1+n_2$

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 {\mathrm{s}}^{-1}$. He told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $\left(0.350\pm 0.005\right) \mathrm{m}$, the gas in the tube is (useful information: $\sqrt{167RT}=640 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}, \sqrt{140RT}=590 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}$. The molar mass $M$ in grams and given in the options. Take the values of $\sqrt{\frac{10}{M}}$ for each gas as given there).