Tag: speed of sound in gas

Quizzes (0) Questions (40)

Questions Related to speed of sound in gas

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

Two open pipes of length $20$ cm and $20.1$ cm produces $10$ beats/s. The velocity of sound in the gas is 

  1. $804 ms^{-1}$
  2. $402 ms^{-1}$
  3. $420 ms^{-1}$
  4. $330 ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For an open pipe, frequency f = v / (2L). Beats = f1 - f2 = (v/2) * (1/L1 - 1/L2). Substituting L1 = 0.2m, L2 = 0.201m, and beats = 10, we get 10 = (v/2) * (1/0.2 - 1/0.201) = (v/2) * (0.001 / 0.0402). Solving for v gives 402 m/s.

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

Which relationship, out of those given below, represents the velocity of sound wave? 

$v=velocity,\ n=frequency,\ \lambda=wave\ length.$

  1. $\displaystyle v=\frac { \lambda }{ n } $
  2. $\displaystyle v=n\lambda $
  3. $\displaystyle v=\frac { n }{ \lambda } $
  4. $\displaystyle v=n\lambda +1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of wave is equal to product of its wavelength and frequency

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

Newton's formula for the velocity of sound in gas is

  1. $\displaystyle v= \sqrt {\frac {P}{\rho}}$
  2. $\displaystyle v= \frac {2}{3}\sqrt {\frac {P}{\rho}}$
  3. $\displaystyle v= \sqrt {\frac {\rho}{P}}$
  4. $\displaystyle v= \sqrt {\frac {2P}{\rho}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Newton's formula for velocity of sound in gas is:

$\displaystyle v= \sqrt {\frac {P}{\rho}}$, where $P$ is pressure & $\rho$ is density of gas

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

Two monatomic ideal gases 1 and 2 of molecular masses  m$ _{1}$  and  m$ _{2}$  respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to gas 2 is given by

  1. $\dfrac{m _{1}}{m _{2}}$
  2. $\sqrt{\dfrac{m _{1}}{m _{2}}}$
  3. $\dfrac{m _{2}}{m _{1}}$
  4. $\sqrt{\dfrac{m _{2}}{m _{1}}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\vartheta =\sqrt{\dfrac{\gamma RT}{M _{0}}}$

$So, \dfrac{\vartheta _{1}}{\vartheta _{2}}=\sqrt{\dfrac{\gamma RT}{M _{01}}}\times \sqrt{\dfrac{M _{02}}{\gamma RT}}$$=\sqrt{\dfrac{M _{02}}{M _{01}}}$$=\sqrt{\dfrac{m _{2}}{m _{1}}}$
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.