Laplace Correction

Q.

The constant $\gamma$ for oxygen as well as for hydrogen is 1.40. If the speed of sound in oxygen is 470 m s${}^{-1}$, what will be the speed in hydrogen at the same temperature and pressure?

1. $1500m{s}^{-1}$

2. $1880m{s}^{-1}$

3. $330m{s}^{-1}$

4. $1000m{s}^{-1}$

Q.

The planet Jupiter has an atmosphere composed mainly of methane at a temperature of $-{130}^{\circ }C$
Find the velocity of sound on the planet. Assume $\gamma$ of the gas inside Jupiter to be 1.3. $(R=8.36Jmo{l}^{-1}{K}^{-1})$

1. 350

2. 420

3. 311

4. 564

Q. Calculate the speed of sound in oxygen from the following data:
Mass of 22.4 litre of oxygen at STP = 32g, $C_V=2.5R$

1. 540 m/s
2. 420 m/s
3. 315 m/s
4. 250 m/s

Q.

A uniform wire of length, $L$, diameter, $D$and density, $\rho$ is stretched under a tension, $T$. The correct relation between its fundamental frequency, $f$, the length, $L$and the diameter, $D$ is

1. $f\propto \frac{1}{LD}$

2. $f\propto \frac{1}{L\sqrt{D}}$

3. $f\propto \frac{1}{D^2}$

4. $f\propto \frac{1}{L{D}^2}$

Q. The velocity of sound in air at a certain temperature is $350m{s}^{-1}$. What will be the velocity of sound in helium at the same temperature? $({\gamma }_{air}=\frac{7}{5})$
[molecular mass of air = 29, molecular mass of helium = 4]

1. 1032 m/s
2. 1100 m/s
3. 925 m/s
4. 1513 m/s

Q.

The absolute temperature of air in a region linearly increases from $T_1$, to $T_2$, in a space of width d. Find the time taken by a sound wave to go through the region in terms of $T_1{T}_2$, d and the speed u of sound at 273 K. Evaluate this time for $T_1\approx 280K,T_3=310K$, d = 33 m and $v=330m{s}^{-1}$.

Q.

At the same temperature and pressure, the ratio of the sound velocity in oxygen to that in hydrogen is about.

1. $16:1$

2. $1:16$

3. $4:1$

4. $1:4$

Q.

Calculate the speed of sound in oxygen from the following data. The mass of $22.4litre$ of oxygen at STP ($T=273K$ and $P=1.0\times {10}^{5}N{m}^{-2}$ ) is $32g$, the molar heat capacity of oxygen at constant volume is $C_v=2.5R$ and that at constant pressure is$C_p=3.5R$

Q. Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP $(T=273KandP=1.0\times {10}^{5}N{m}^{-2})$ is 32g, the molar heat capacity of oxygen at constant volume is $C_V$ = 2.5 R and that at constant pressure is Cp = 3.5 R.

1. 365m/s

2. 300m/s

3. 315m/s

4. 350m/s

Q.

An ideal gas having density $1.7\times {10}^{-3}gc{m}^{-3}$ at a pressure $1.5\times {10}^5$ Pa is filled in a Kundt tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capaticies $C_p$ and $C_v$ of the gas.

Q.

At what temperature will the speed of sound in hydrogen be the same as in oxygen at 100${}^{\circ }$ C? Molar masses of oxygen and hydrogen are in the ratio 16:1.

1. 273 k

2. 23 k

3. 300 k

4. 50 k

Q. The velocity of sound in oxygen is less than in helium.

1. True
2. False

Q. Calculate the speed of sound in oxygen from the following data:
Mass of 22.4 litre of oxygen at STP = 32g, $C_V=2.5R$

1. 540 m/s
2. 420 m/s
3. 315 m/s
4. 250 m/s

Q. The string of a sonometer is divided into two parts with the help of wedge. The total length of the string is $1m$ and the two parts differ in length by $2mm$. When sounded together, they produce two beats. The frequencies of the notes emitted by the two parts are

1. none of these
2. $501$ and $503$
3. $501$ and $499$
4. $499$ and $497$

Q. State Newton's formula for the velocity of sound in a gas. What is the Laplace's correction?

Q. The velocity of sound in air at a certain temperature is $350m{s}^{-1}$. What will be the velocity of sound in helium at the same temperature? $({\gamma }_{air}=\frac{7}{5})$
[molecular mass of air = 29, molecular mass of helium = 4]

1. 1032 m/s
2. 1100 m/s
3. 925 m/s
4. 1513 m/s

Q. Two open pipes, whose lengths are $50cm$ and $51cm$ respectively, produce five beat per second when sounded together. The fundamental frequencies in Hertz will be

1. $65and60$
2. $90and95$
3. $95and90$
4. $255and250$

Q. Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP $(T=273KandP=1.0\times {10}^{5}N{m}^{-2})$ is 32g, the molar heat capacity of oxygen at constant volume is $C_V$ = 2.5 R and that at constant pressure is Cp = 3.5 R.

1. $300\frac{m}{s}$
2. $315\frac{m}{s}$
3. $350\frac{m}{s}$
4. $365\frac{m}{s}$

Q. The isothermal elasticity of a medium is E${}_i$ and the adiabatic elasticity in E${}_a$ . The velocity of sound in the medium is proportional to

1. $E_j$
2. $\sqrt{E_i}$
3. $E_a$
4. $\sqrt{E_a}$

Q. A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire id 50 N and the speed is $320m{s}^{-1}$, the mass of the string is ___ gram

1. 5
2. 10
3. 20
4. 40

Q. Air is blown at the mouth of a tube of length 25 cm and diameter equal to 2 cm open at both ends. If velocity of sound in air is 330 ms${}^{-1}$ the sound emitted will have all the frequencies in the group (neglect end correction)

1. 330, 990, 1690 Hz
2. 660, 1320, 1980 Hz
3. 302, 664, 1320 Hz
4. 660, 1000, 3300 Hz

Q. If two air columns of lengths $100cm$ and $101cm$ sounding in their fundamental note gave $17$ beats in $20$ seconds, then the velocity of sound will be

1. $300m/s$
2. $343.4m/s$
3. $250m/s$
4. $277.8m/s$

Q. The velocity of sound in air is $350m/s$. The fundamental frequency of an open organ pipe of length $50cm$ will be

1. $700/s$
   
2. $350/s$
   
3. $175/s$
   
4. $900/s$

Q. Suppose a spherical loudspeaker emits sound isotropically at $10W$ into a room with completely absorbent walls, floor, and ceiling (an anechoic chamber).
What is the intensity of the sound at distance $d=3.0m$ from the center of the source?

Q.

The speed of sound in hydrogen at $0^{0}C$ is 1280 $m{s}^{-1}$. The desiny of hydrogen at STP is 0.089 kg $m^{-3}$. Calculate the molar heat capacities $C_p$ and $C_v$ of hydrogen.

Q. The ratio of the velocity of sound in a monatomic gas to that in a triatomic gas having same molar mass, under similar conditions of temperature and pressure, is

1. 1.5
2. 1.62
3. 1.12
4. 1.25

Q.

The planet Jupiter has an atmosphere composed mainly of methane at a temperature of $-{130}^{\circ }C$
Find the velocity of sound on the planet. Assume $\gamma$ of the gas inside Jupiter to be 1.3. $(R=8.36Jmo{l}^{-1}{K}^{-1})$

1. 350

2. 420

3. 311

4. 564

Q. The velocity of a particle in SHM at the instant when it is $0.6$ cm away from the mean position is $4$ cm /sec. If the amplitude of vibration is $1$ cm then its velocity at the instant when it is $0.8$cm away from the mean position is:

1. $3.0$ cm/s
2. $2.5$ cm/s
3. $2.25$ cm/s
4. $3.5$ cm/s

Q. The lengths of two closed organ pipes are 0.770 m. If they are sounded together , 3 beats per second are produced . the velocity of sound will be $:-$

1. 350.5 m/sec
2. 335.5 m/sec
3. 346.5 m/sec
4. none of these

Q.

1. 9
2. 12
3. 16
4. 18