Tag: waves

Quizzes (32) Questions (233)

Questions Related to waves

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

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

  1. adiabatic

  2. isothermal

  3. isochoric

  4. isobaric
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $13:3$
  2. $4:3$
  3. $2:1$
  4. $4:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 } $

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

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?

  1. $\dfrac {a\omega _{1}}{b\omega _{2}}$
  2. $\dfrac {ab\omega _{1}}{\omega _{2}}$
  3. $\dfrac {b\omega _{1}}{a\omega _{2}}$
  4. $\dfrac {\omega _{1}}{ab\omega _{2}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Power P is proportional to (pressure amplitude)^2 * frequency^2. Given sqrt(P1/P2) = a and (deltaP1/deltaP2) = b, then (a)^2 = (b)^2 * (omega1/omega2)^2. Rearranging gives omega1/omega2 = a/b. The ratio of frequencies is proportional to the ratio of angular frequencies.

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

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

  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. $\begin{array} { l } { y = 3 \times 10 ^ { 2 } \sin \pi ( 340 t - x ) } \\ { I = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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