Wave Speed

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

Q. A sound wave of frequency $600\text{Hz}$ falls normally on a perfect reflecting wall. The minimum distance from the wall at which the particles of the medium will have maximum displacement during their 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.

As the wavelength of a wave in a uniform medium increases, then what will happen with its frequency?

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

1. 
2. 
3. 
4. 

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. 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. 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 a gas at a temperature ${27}^{\circ }\text{C}$ is $v$. In the same gas, its velocity will be $2v$ at temperature

1. ${727}^{\circ }\text{C}$
2. ${827}^{\circ }\text{C}$
3. ${927}^{\circ }\text{C}$
4. ${627}^{\circ }\text{C}$

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

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

1. 
2. 
3. 
4. 

Q. A tuning fork with a time period of $\frac{1}{256}\text{s}$ produces a sound wave in which the separation between adjacent compression and rarefaction is $0.7\text{m}$. Then, the speed of sound wave is

1. $250\text{m/s}$
2. $400\text{m/s}$
3. $310\text{m/s}$
4. $358\text{m/s}$

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

Q. Which of the following quantities related to a sound wave affect the velocity of sound in a gaseous medium?

1. Amplitude
2. Frequency
3. Phase Angle
4. Temperature of the medium

Q. A sound wave is propagating through a medium following an adiabatic process . Imagine that after some time, it starts following an isothermal process. ($V_{iso}$ is the speed of sound when it follows isothermal process and $V_{ad}$ is the speed of sound when it follows adiabatic process). Then

1. $V_{ad}<V_{iso}$
2. $V_{ad}=V_{iso}$
3. $V_{ad}>V_{iso}$
4. None of these

Q. A stone is dropped from the top of a tower of $500\text{m}$ height, into a pond of water at the base of the tower. When is the splash heard at the top?

$(\text{Given}g=10{\text{ms}}^{-2}$ and speed of sound $=340{\text{ms}}^{-1})$

1. $10\text{s}$
2. $11.47\text{s}$
3. $1.10\text{s}$
4. $20\text{s}$

Q. In sound wave, $V_w$ is the wave velocity and $V_p$ is particle velocity. Then:

1. ${\overrightarrow{V}}_w||{\overrightarrow{V}}_p$
2. ${\overrightarrow{V}}_w\perp {\overrightarrow{V}}_p$
3. ${\overrightarrow{V}}_w\times {\overrightarrow{V}}_p=0$
4. ${\overrightarrow{V}}_w.{\overrightarrow{V}}_p=0$

Q. Speed of a longitudinal wave in air is $300\text{m/s}$ and in steel is $3000\text{m/s}$. If wavelength in air is $0.5\text{m}$ , then its wavelength in steel is

1. $5\text{m}$
2. $10\text{m}$
3. $15\text{m}$
4. $20\text{m}$

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

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. A sound wave is propagating through a medium following an adiabatic process . Imagine that after some time, it starts following an isothermal process. ($V_{iso}$ is the speed of sound when it follows isothermal process and $V_{ad}$ is the speed of sound when it follows adiabatic process). Then

1. $V_{ad}<V_{iso}$
2. $V_{ad}=V_{iso}$
3. $V_{ad}>V_{iso}$
4. None of these

Q. A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 Mhz. The speed of sound in a tissue is 1.7 km/s. The wave length of sound in a tissue close to

1. $4\times {10}^{-4}m$
2. $8\times {10}^{-4}m$
3. $4\times {10}^{-3}m$
4. $8\times {10}^{-3}m$

Q. Distance between successive compression and rarefaction in a sound wave is $1\text{m}$. If the 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 tuning fork with a time period of $\frac{1}{256}\text{s}$ produces a sound wave in which the separation between adjacent compression and rarefaction is $0.7\text{m}$. Then, the speed of sound wave is

1. $250\text{m/s}$
2. $400\text{m/s}$
3. $310\text{m/s}$
4. $358\text{m/s}$

Q. Which of the following quantities related to a sound wave affect the velocity of sound in a gaseous medium?

1. Amplitude
2. Frequency
3. Phase Angle
4. Temperature of the medium

Q. A Kundt's tube apparatus has a copper rod of length $0.8\text{m}$ clamped at $40\text{cm}$ from one of the ends. The tube contains air in which the speed of sound is $330\text{m/s}$. The powder collected in the heaps are separated by a distance of $6\text{cm}$. What is the speed of sound wave in a copper rod?

1. $8.8\text{km/s}$
2. $3.4\text{km/s}$
3. $4.4\text{km/s}$
4. $6.8\text{km/s}$

Q. A sound wave of wavelength $4\text{mm}$ is produced in air, and it travels at a speed of $300\text{m/s}$. Will it be audible?

1. Yes
2. No
3. Sometimes audible & sometimes inaudible
4. Can't say

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. $\sqrt{\frac{Y}{\rho n}}$
2. $\sqrt{\frac{Y}{\rho n^{1/2}}}$
3. $\sqrt{\frac{Y}{\rho }}$
4. $\sqrt{\frac{Y}{\rho n^{3/2}}}$