Tag: waves

Questions Related to waves

Two gases with different densities and same ratio of specific heats $(\gamma)$ are mixed in proportions $V _1$ and $V _2$ by volume. The velocity $C$ of sound in mixture will be given by $(C _1, \space C _2$ are velocities in individual gases$)$

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. $\displaystyle\frac{C _1+C _2}{2}$

  2. $\sqrt{C _1C _2}$

  3. $\displaystyle\frac{C _1C _2\sqrt{(V _1+V _2)}}{\sqrt{(V _1C _2^2+V _2C _1^2)}}$

  4. $\displaystyle\frac{C _1C _2\sqrt{(V _1+V-2)}}{\sqrt{(V _1C _1^2+V _2C _2^2)}}$

Show answer
Correct Option: C
Explanation:
$C _1=\sqrt{\dfrac{\gamma P}{\rho _1}}$ and $C _2=\sqrt{\dfrac{\gamma P}{\rho _2}}$

$\rho _1=\dfrac{\gamma P}{{C _1}^2}$

$\rho _2=\dfrac{\gamma P}{{C _2}^2}$
Mixture density, 
$\rho=\dfrac{\rho _1 \times V _1 + \rho _2 \times V _2}{V _1 + V _2}$

$\rho=\dfrac{\dfrac{\gamma P}{{C _1}^2} \times V _1 + \dfrac{\gamma P}{{C _2}^2} \times V _2}{V _1 + V _2}$

$\rho={\gamma P} \dfrac{\dfrac{1}{{C _1}^2} \times V _1 + \dfrac{1}{{C _2}^2} \times V _2}{V _1 + V _2}$

$C=\sqrt{\dfrac{\gamma P}{\rho}} = \sqrt{\dfrac{1}{\dfrac{\dfrac{1}{{C _1}^2} \times V _1 + \dfrac{1}{{C _2}^2} \times V _2}{V _1 + V _2}}}$

$C = C _1 C _2 \sqrt{\dfrac{V _1+V _2}{V _1 C _2^2+V _2 C _1^2}}$

Standing waves of frequency 5.0 KHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities ${ C } _{ p }$   and ${ C } _{ v }$ of the gas.

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. $20.7J/molK,29.0J/molK$

  2. $29.0J/molK,20.7J/molK$

  3. $2.90J/molK,2.07J/molK$

  4. none of these

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Correct Option: A

The echo of a gunshot is heard 8 s after the gun is fired. How far from a person is the surface that reflects the sound (velocity of sound in air = $350 m/s)$?

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. 1400 m

  2. 2800 m

  3. 700 m

  4. 350 m

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Correct Option: B

The speed of sound in hydrogen at $  N T P,  $ is 1270 $ \mathrm{m} / \mathrm{s} .$ Then the speed in a mixture of hydrogen and oxigen in the ratio $  4 : 1  $ by volume, (in $  m / s )  $ will be

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. 635

  2. 318

  3. 158

  4. 1270

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Correct Option: A

The speed of sound in an ideal gas at ${ T } _{ 1 }$ K and   ${ T } _{ 2 }$K  are $ { V } _{ 1 }$ and $ { V } _{ 2 }$ respectively. if the root mean square velocity of molecules of same gas at these temperatures are  $  { v } _{ rms1 }  $ and${ v } _{ rms1 }$ respectively, then 

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. ${ v } _{ rms2 }={ v } _{ rms1 }\left( \dfrac { { v } _{ 2 } }{ { v } _{ 1 } } \right) $

  2. ${ v } _{ rms2 }={ v } _{ rms1 }\left( \dfrac { { v } _{ 1 } }{ { v } _{ 2 } } \right) $

  3. $ { v } _{ rms2 }={ v } _{ rms1 }\left( \sqrt { \dfrac { { v } _{ 2 } }{ { v } _{ 1 } } } \right) $

  4. $ { v } _{ rms2 }={ v } _{ rms1 }\left( \sqrt { \dfrac { { v } _{ 1 } }{ { v } _{ 2 } } } \right) $

Show answer
Correct Option: D

As per Newton's formula velocity of sound , at NTP is 

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. 340 m/s

  2. 332.3 m/s

  3. 279.9m/s

  4. 290 m/s

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Correct Option: B

The relation between velocity of sound in gas $(v)$ and r.m.s velocity of molecules of gas $v _{r.m.s}$ is

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. $v=v _{r.m.s}(\gamma/ 3)^{1/2} $

  2. $v _{r.m.s}=v(2/3)^{1/2} $

  3. $v=v _{r.m.s} $

  4. $ v=v _{r.m.s}(3/\gamma)^{1/2}$

Show answer
Correct Option: A
Explanation:

Velocity of sound in a gas is

$v=\sqrt{\dfrac{\gamma P}{\rho}}$

and from $P=\dfrac{1}{3}\rho v _{rms}^2$

$v _{rms}=\sqrt{\dfrac{3P}{\rho}}$
Thus

$\dfrac{v}{v _{rms}}=\sqrt{\dfrac{\gamma}{3}}$

Ans: A

The velocity of sound in air is $330$ m/s. The r.m.s velocity of air molecules $(\gamma=1.4) $ is approximately equal to

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. 400 m/s

  2. 471.4 m/s

  3. 231 m/s

  4. 462 m/s

Show answer
Correct Option: B
Explanation:

$v _{air}=\sqrt{\dfrac{\gamma RT}{M}}=330m/s$

$v _{rms}=\sqrt{\dfrac{3RT}{M}}$
$=\sqrt{\dfrac{3}{\gamma}}\times 330m/s$
$\gamma=1.4$
$\implies v _{rms}=471.4m/s$

The velocity of sound in a gas at pressure $P$ and density $d$ is

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. $\displaystyle v= \sqrt {\frac {\gamma P}{d}}$

  2. $\displaystyle v= \sqrt {\frac {P}{\gamma d}}$

  3. $\displaystyle v= \gamma \sqrt {\frac {P}{d}}$

  4. $\displaystyle v= \sqrt {\frac {2 P}{d}}$

Show answer
Correct Option: A
Explanation:

$\displaystyle v= \sqrt {\frac {\gamma RT}{M}}$

$PV=RT$

$\displaystyle P\frac {M}{d}=RT$

$\displaystyle \frac {P}{d} = \frac {RT}{M}$

$\displaystyle v= \sqrt {\frac {\gamma P}{d}}$

Does the sound of an explosion travel faster than the sound produced by a humming bee?

speed of sound in gas speed of a travelling wave oscillation and waves waves physics

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

$No$


The speed of sound depends only on the physical conditions of the medium in which the sound is travelling and the speed and direction of the wind present if any.
The speed of the sound doesn't depend on its loudness.

Hence although the sound of explosion is much louder than the humming of a bee, both sounds travel with equal speed.