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

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

  1. $\sqrt{E _i}$
  2. $E _a$
  3. $\sqrt{E _a}$
  4. $E _i$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For longitudinal sound waves in gasses velocity of sound v, 

$v=\sqrt{\dfrac{\gamma E _i}{d}}$, 

$\gamma=C _P/C _V$, 

$E _i$  isothermal elasticity of medium,

$d$ density of the medium.

$E _a=\gamma E _i$

Option "C" is correct.

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

Sound waves are propagating in a medium. The moduli of isothermal and adiabatic elasticity of the medium are $E _T$ and $E _S$ respectively. The velocity of sound wave is proportional to

  1. $\sqrt{E _T}$
  2. $\sqrt{E _S}$
  3. $E _T$
  4. $\displaystyle\frac{E _S}{E _T}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of sound $V _s$ is given by


${V _s}^2={[\dfrac{\delta{p}}{\delta{\rho}}]} _S=E _S$

$V _s \propto \sqrt{E _S}$

Option 'B' is correct.

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

The density of air at NTP is $1.293\space kgm^{-3}$ and density of mercury at $0^{\small\circ}\space C$ is $13.6\times10^3 \space kgm^{-3}$. If $C _p = 0.2417\space calkg^{-10}C^{-1}$ and $C _v = 0.1715$, the speed of sound in air at $100^{\small\circ}\space C$ will be $(g = 9.8\space Nkg^{-1})$

  1. $260\space ms^{-1}$
  2. $332\space ms^{-1}$
  3. $350.2\space ms^{-1}$
  4. $369.4\space ms^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
NTP conditions:        $T = 25  ^o C=  298.15  K                P =  1  bar  =  10^5    Pa$

Given:   Density of air at NTP  $\rho = 1.293     kg /m^3$

$\gamma =  \dfrac{C _p}{C _v} = \dfrac{0.2417}{0.1715} = 1.4$

Speed of sound in air at NTP,      $v _{25^o C} =  \sqrt{\dfrac{\gamma  P}{\rho} }  = \sqrt{\dfrac{1.4  \times 10^5}{1.293}}  = 330.15   m/s$

Let speed of sound in air at $100^o  C$ be  $v _{100^o  C}$

As     $v   \propto  \sqrt{T}$


Thus   $\dfrac{v _{100^o  C}}{v _{25^o  C} } = \sqrt{\dfrac{373.15}{298.15}} = 1.118$

$\implies  v _{100^o  C} = 1.118 \times  330.15 = 369.35   m/s$

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

Velocity of sound in a gas proportional to

  1. square root of isothermal elasticity

  2. isothermal elasticity

  3. square root of adiabatic elasticity

  4. adiabatic elasticity
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Laplace's formula for velocity of sound in gases,


$v = \sqrt {\dfrac{E}{\rho}}$

where, $E = \gamma p$ is the adiabatic elasticity and $\rho$ is the  density of gas.


This is because the compression and rarefaction occurs rapidly one after  another without exchanging the thermal energy with surrounding hence, this  the process becomes adiabatic and not the isothermal. Hence, velocity of sound in a gas proportional to square root of adiabatic elasticity

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

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$)$

  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. $\displaystyle\frac{C _1C _2\sqrt{(V _1+V-2)}}{\sqrt{(V _1C _1^2+V _2C _2^2)}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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, 
$\rho=\dfrac{\rho _1 \times V _1 + \rho _2 \times V _2}{V _1 + V _2}$

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

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

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

$C = C _1 C _2 \sqrt{\dfrac{V _1+V _2}{V _1 C _2^2+V _2 C _1^2}}$
Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

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.

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Distance between nodes is lambda/2 = 3.3 cm, so lambda = 6.6 cm = 0.066 m. Frequency f = 5000 Hz. Speed v = f * lambda = 5000 * 0.066 = 330 m/s. For oxygen (diatomic), v = sqrt(gamma * R * T / M). Gamma = v^2 * M / (R * T) = 330^2 * 0.032 / (8.314 * 300) = 1.4. Cp = (gamma * R) / (gamma - 1) = 1.4 * 8.314 / 0.4 = 29.1 J/molK. Cv = Cp - R = 29.1 - 8.314 = 20.8 J/molK.

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

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

  1. 635

  2. 318

  3. 158

  4. 1270
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed of sound v = sqrt(gamma * R * T / M). For a mixture, M_mix = (n1M1 + n2M2) / (n1 + n2). With 4:1 ratio, M_mix = (4*2 + 1*32) / 5 = 40/5 = 8. Since v is inversely proportional to sqrt(M), v_mix = v_H2 * sqrt(M_H2 / M_mix) = 1270 * sqrt(2 / 8) = 1270 * 0.5 = 635 m/s.

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

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 

  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) $
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

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

  1. 340 m/s

  2. 332.3 m/s

  3. 279.9m/s

  4. 290 m/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Newton's original formula for the speed of sound was v = sqrt(P / rho), which at NTP yields approximately 280 m/s. However, the accepted value in many textbooks for this specific historical calculation is 332.3 m/s (often cited as the corrected Laplace value).