Wave Speed

Q. The speed of longitudinal wave is given by $v=\sqrt{\frac{E}{\rho }}$ where $\rho$ is the density of the medium. Match the following columns for the quantities represented by $E$ in different media.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Solid}& \text{(p)}& \text{Bulk modulus}\\ \text{(B)}& \text{Liquid}& \text{(q)}& \text{Shear modulus}\\ \text{(C)}& \text{Gas}& \text{(r)}& \text{Young's modulus}\end{array}$

1. $A\to p,B\to q,C\to r$
2. $A\to r,B\to q,C\to p$
3. $A\to r,B\to p,C\to q$
4. $A\to q,B\to r,C\to p$

Q. Which of the following graphs represent the correct variation of velocity $\left(v\right)$ of sound with the pressure $\left(P\right)$ in a gas at constant temperature?

1. 
2. 
3. 
4. 

Q.

A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

Q. Distance between successive compression and rarefaction is $1\text{m}$ and velocity of sound is $360{\text{ms}}^{-1}.$ Find the frequency of sound wave.

1. $180\text{Hz}$
2. $160\text{Hz}$
3. $150\text{Hz}$
4. $120\text{Hz}$

Q. A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperture of ${27}^{o}C$, two successive resonances are produced at $20cm$ and $73cm$ of column length. If the frequency of the tuning fork is $320Hz$, the velocity of sound in air at ${27}^{o}C$ is approximately

1. $339m/s$
2. $330m/s$
3. $350m/s$
4. $300m/s$

Q.

A bat emits ultrasonic sound of frequency 1000 kHz in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is $340m{s}^{-1}$ and in water $1486m{s}^{-1}$.

Q. The speed of sound in a mixture of $1$ mole of helium and $2$ moles of oxygen at $27{}^{\circ }\text{C}$
will be

1. $501\text{m/s}$
2. $201\text{m/s}$
3. $401\text{m/s}$
4. $301\text{m/s}$

Q. The speed of sound in hydrogen gas at $\text{STP}$ is $v_o$. The speed of sound in a mixture containing $3$ parts of hydrogen gas and $2$ parts of oxygen gas at $\text{STP}$ will be

1. $\frac{v_o}{\sqrt{5}}$
2. $\frac{v_o}{\sqrt{3}}$
3. $\frac{v_o}{\sqrt{7}}$
4. $\frac{v_o}{\sqrt{6}}$

Q.

A glass tube of length $1.0m$ is completely filled with water. A vibrating tuning fork of frequency $500Hz$ is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If the velocity of sound in air is $330m{s}^{-1}$, then the total number of resonances, that occur will be

1. $2$

2. $3$

3. $1$

4. $5$

5. $4$

Q. If velocity of sound in a gas is 360 m/s and the distance between a compression and the nearest rarefaction is 1 m, then the frequency of sound is

1. 90 Hz
2. 180 Hz
3. 360 Hz
4. 720 Hz

Q. A string fixed at both ends is vibrating in seventh harmonic. How many nodes and antinodes are set up in it respectively?

1. $8,7$
2. $7,7$
3. $8,9$
4. $9,8$

Q.

A tuning fork of frequency 440 Hz is attached to a long string of linear mass density $0.01kg{m}^{-1}$ kept under a tension of 49 N. The fork produces transverse waves of amplitude 0.50 mm on the string. (a) Find the wave speed and the wavelength of the waves. (b) Find the maximum speed and acceleration of a particle of the string. (c) At what average rate is the tuning fork tranmitting energy to the string ?

Q. A sound wave of frequency $500\text{Hz}$ covers the distance of $1000\text{m}$ in $5\text{s}$ between points $x$ and $y$. The number of wavelengths between $x$ and $y$ are

1. $1500$
2. $1000$
3. $2500$
4. $5000$

Q. A bat emits ultrasonic sound of frequency $100\text{kHz}$ in air. If the sound gets reflected (without transmission and loss of energy) from a water surface then wavelength of the reflected sound is
[speed of sound in air is $340{\text{ms}}^{-1}$]

1. $0.55\times {10}^{-2}\text{m}$
2. $0.34\times {10}^{-2}\text{m}$
3. $0.65\times {10}^{-2}\text{m}$
4. $0.74\times {10}^{-2}\text{m}$

Q. The velocity of sound in hydrogen is $1400m{s}^{-1}$. What will be the velocity of sound in a mixture of gases having two parts by volume of hydrogen and one part by volume of oxygen. Maintaing the same pressure?

1. 471.4 m/s
2. 571.4 m/s
3. 371.4 m/s
4. 671.4 m/s

Q. Light can travel in vacuum but not sound because

1. speed of sound is very smaller than speed of light
2. light waves are electromagnetic in nature
3. speed of light is very high
4. sound waves are electromagnetic in nature

Q.

A boat at anchor is rocked by waves whose crests are $100\mathrm{m}$ apart and velocity is $25{\mathrm{ms}}^{-1}$. The boat bounces up once in every:

1. $2500\mathrm{s}$

2. $75\mathrm{s}$

3. $4\mathrm{s}$

4. $0.25\mathrm{s}$

Q. When the temperature of an ideal gas is increased by $600\text{K}$, the speed of sound in it become $\sqrt{3}$ times the initial speed. The initial temperature of the gas is

1. $200\text{K}$
2. $300\text{K}$
3. $400\text{K}$
4. $500\text{K}$

Q.

The equation of a travelling sound wave is y =6.0 sin (600 -1.8 x) where y is measured in ${10}^{-5}$m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.

Q.

Two wires of different densities but same area of cross section are sodered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

Q.

In the arrangement shown in figure (15-E6), the string has a mass of 4.5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley ? Take $g=10m{s}^{-2}$.

Q.

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is/are

1. 
   the average energy per mole of the gas mixture is $2RT$.
2. 
   the ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6/5}$.
3. 
   the ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.
4. 
   the ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/$\sqrt{2}$.

Q. For a transverse wave travelling along a straight line, the distance between two peaks (crests) in $5\text{m},$ while the distance between one crest and one trough is $1.5\text{m}.$ The possible wavelengths (in $\text{m}$) of the waves are-

1. $1,3,5,.....$
2. $\frac{1}{1},\frac{1}{3},\frac{1}{5},......$
3. $1,2,3,.....$
4. $\frac{1}{2},\frac{1}{4},\frac{1}{6},......$

Q. Sound wave of frequency $600\text{Hz}$ fall normally on a perfect reflecting wall. The minimum distance from the wall at which particles of the medium will have maximum displacement during its vibrations is
[speed of sound $=300\text{m/s}$]

1. $\frac{7}{8}\text{m}$
2. $\frac{3}{8}\text{m}$
3. $\frac{1}{8}\text{m}$
4. $\frac{5}{8}\text{m}$

Q. At $t=0$, a transverse wave pulse travelling along positive $x-$direction with speed $3m/s$ in a string described by the function $y=\frac{9}{x^2}$ given that $x\ne 0$. Transverse velocity of particle at $x=3m$ and $t=3s$ will be

1. $-\frac{1}{8}\frac{m}{s}$
2. $\frac{1}{4}\frac{m}{s}$
3. $-\frac{1}{4}\frac{m}{s}$
4. $\frac{1}{2}\frac{m}{s}$

Q. The density of air at $NTP$ is $1.3\text{g/L}$. Assuming air to be diatomic with $\gamma =1.4$, calculate the velocity of sound in air at ${27}^{\circ }\text{C}$.

1. $330\text{m/s}$
2. $346\text{m/s}$
3. $300\text{m/s}$
4. $660\text{m/s}$

Q. Calculate the speed of sound in a gas in which two waves of wavelength 1.00m and 1.01m produce 30beats in 10seconds

1. 313 m/s
2. 300 m/s
3. 303 m/s
4. 310 m/s

Q. Length of a string of density ρ and Young’s modulus Y under tension is increased by $\frac{1}{n}$ times of its original length. If the velocity of transverse and longitudinal vibrations of the string is same, find the value of such velocity.

1. 
2. 
3. 
4. 

Q. A stone is dropped into a lake by a man from a tower of height $500\text{m}$. The sound of the splash will be heard by the man after
[velocity of sound in air $=340{\text{ms}}^{-1}$]

1. $21.5\text{s}$
2. $10.5\text{s}$
3. $11.5\text{s}$
4. $14.5\text{s}$

Q. A sound wave travels a distance $l$ in helium gas in time $t$ at a particular temperature. If at the same temperature a sound wave is propagated in oxygen gas, it will cover the same distance $l$ in time (approximately)

1. $2t$
2. $3t$
3. $4t$
4. $5t$