Tag: waves

Questions Related to waves

In deriving the speed of sound in air, Newton assumed that the wave travels in 

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

  1. Adiabatic condition

  2. Isothermal condition

  3. Isobaric condition

  4. Isoclinic condition

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Correct Option: B
Explanation:

The sound propogation according to Newton takes place in isothermal condition

The correct option is (b)

According to Newton, when sound propogates in air, the temperature variation in the medium is

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

  1. Zero

  2. 10 C

  3. 5 C

  4. 1 C

Show answer
Correct Option: A
Explanation:

The sound propogation according to Newton takes place in isothermal condition. Hence no temperature change happens or temperature change is zero

The correct option is (a)

The formula proposed by Newton for velocity of sound in air is based on _________ process.

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

  1. adiabatic

  2. isothermal

  3. isochoric

  4. isobaric

Show answer
Correct Option: B
Explanation:

According to Newton, when sound waves propagate in air, compression and rarefaction are formed. He assumed that the process is very slow and the heat produced during compression is given to surrounding and heat loss during compression is gained from surrounding. So the temperature remains constant and sound waves propagate through an isothermal process. 

so the answer is B.

The speed of a longitudinal wave in a mixture of hellium and neon at 300 k was found to be 758 m/s. The composition of the mixture would then be

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

  1. $13:3$

  2. $4:3$

  3. $2:1$

  4. $4:1$

Show answer
Correct Option: A
Explanation:

When ${M} _{1}=0.004kg/mol$) is mixed with ${n} _{2}$ moles of (${M} _{2}=0.020kg/mol$), the equivalent molar mass of mix would be:

$M'=\cfrac{{n} _{1}{M} _{1}+{n} _{2}{M} _{2}}{{n} _{1}+{n} _{2}}=\cfrac{4{n} _{1}+20{n} _{2}}{1000({n} _{1}+{n} _{2})}$
Both $He$ and $Ne$ are monoatomic so for mixture $\gamma =\cfrac{5}{3}$
so, the velocity of sound
$V=\sqrt { \cfrac { rRT }{ M' }  } \Rightarrow M'=\cfrac { \gamma RT }{ { V }^{ 2 } } \left( at\quad T=300K \right) \quad $
$\Rightarrow \cfrac { 4{ n } _{ 1 }+20{ n } _{ 2 } }{ 1000\left( { n } _{ 1 }+{ n } _{ 2 } \right)  } =\cfrac { 5\times 8.31\times 300 }{ 3\times { (758) }^{ 2 } } \simeq \cfrac { 7 }{ 1000 } \Rightarrow \cfrac { { n } _{ 1 } }{ { n } _{ 2 } } \simeq 4.33=\cfrac { 13 }{ 3 } $

Two sound waves of angular frequencies $\omega _{1}$ and $\omega _{2}$ move in the same direction. If the under-root of ratio of average power transmitted across a cross-section by them is a and the ratio of their pressure amplitude is $b$, find the ratio of their frequencies of vibrations?

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

  1. $\dfrac {a\omega _{1}}{b\omega _{2}}$

  2. $\dfrac {ab\omega _{1}}{\omega _{2}}$

  3. $\dfrac {b\omega _{1}}{a\omega _{2}}$

  4. $\dfrac {\omega _{1}}{ab\omega _{2}}$

Show answer
Correct Option: C

A Sound wave with an amplitude of $ 3 \mathrm { cm }$ starts towards right from origin and gets reflected at a rigid wall after a second. If the velocity of  the wave is $ 340 \mathrm { ms } ^ { - 1 }$  and it has a wavelength of $ 2 \mathrm { m } $, the equations of incident and reflected waves respectively could be

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

  1. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) } \ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$

  2. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) } \ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$

  3. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) } \ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) \text { towards left } } \end{array}$

  4. $\begin{array} { l } { y = 3 \times 10 ^ { 2 } \sin \pi ( 340 t - x ) } \ { I = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { \omega t-kx } \right)  \ \lambda =2m=\frac { { 2\pi  } }{ k }  \ \Rightarrow k=\pi  \ v=340\, m/s \ w=vk \ =240\pi  \ Now, \ y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t-\pi x } \right) \, \, towards\, right \ and, \ y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t+\pi x+\pi  } \right)  \ =-\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t+\pi x } \right) \, \, \, \, \, \, \, towards\, \, left \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

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 :

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

  1. $\sqrt{E _i}$

  2. $E _a$

  3. $\sqrt{E _a}$

  4. $E _i$

Show answer
Correct Option: C
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.

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

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

  1. $\sqrt{E _T}$

  2. $\sqrt{E _S}$

  3. $E _T$

  4. $\displaystyle\frac{E _S}{E _T}$

Show answer
Correct Option: B
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.

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 $(g = 9.8\space Nkg^{-1})$

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

  1. $260\space ms^{-1}$

  2. $332\space ms^{-1}$

  3. $350.2\space ms^{-1}$

  4. $369.4\space ms^{-1}$

Show answer
Correct Option: D
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   $\dfrac{v _{100^o  C}}{v _{25^o  C} } = \sqrt{\dfrac{373.15}{298.15}} = 1.118$

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

Velocity of sound in a gas proportional to

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

  1. square root of isothermal elasticity

  2. isothermal elasticity

  3. square root of adiabatic elasticity

  4. adiabatic elasticity

Show answer
Correct Option: C
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