Tag: speed of a travelling wave

Questions Related to speed of a travelling wave

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

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

  1. $804 ms^{-1}$

  2. $402 ms^{-1}$

  3. $420 ms^{-1}$

  4. $330 ms^{-1}$

Show answer
Correct Option: B

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

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

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

  1. $\displaystyle v=\frac { \lambda }{ n } $

  2. $\displaystyle v=n\lambda $

  3. $\displaystyle v=\frac { n }{ \lambda } $

  4. $\displaystyle v=n\lambda +1$

Show answer
Correct Option: B
Explanation:

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

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

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

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

Show answer
Correct Option: A
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

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

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

  1. $\dfrac{m _{1}}{m _{2}}$

  2. $\sqrt{\dfrac{m _{1}}{m _{2}}}$

  3. $\dfrac{m _{2}}{m _{1}}$

  4. $\sqrt{\dfrac{m _{2}}{m _{1}}}$

Show answer
Correct Option: D
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}}}$

Newton assumes that sound propagation in gas takes under

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

  1. isothermal condition

  2. adiabatic condition

  3. isobaric condition

  4. isentropic condition

Show answer
Correct Option: A
Explanation:

Newton assumed that sound propagation in a gas takes under isothermal condition.

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

Show answer
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