Physics · Science General

Acoustics and Sound Waves

2,160 Questions

Acoustics and sound waves deal with mechanical vibrations traveling through media like air and water. Key concepts include wave reflection, beats, echoes, the Mach number, and infrasound. These physics fundamentals are regularly tested in general science sections of multiple competitive exams.

Sound wave propagationEchoes and reflectionWave interferenceMach numberInfrasound frequency

Acoustics and Sound Waves Questions

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

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

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

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).

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

The velocity of sound in air is $330$ m/s. The r.m.s velocity of air molecules $(\gamma=1.4) $ is approximately equal to

  1. 400 m/s

  2. 471.4 m/s

  3. 231 m/s

  4. 462 m/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$v _{air}=\sqrt{\dfrac{\gamma RT}{M}}=330m/s$

$v _{rms}=\sqrt{\dfrac{3RT}{M}}$
$=\sqrt{\dfrac{3}{\gamma}}\times 330m/s$
$\gamma=1.4$
$\implies v _{rms}=471.4m/s$

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

Does the sound of an explosion travel faster than the sound produced by a humming bee?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$No$


The speed of sound depends only on the physical conditions of the medium in which the sound is travelling and the speed and direction of the wind present if any.
The speed of the sound doesn't depend on its loudness.

Hence although the sound of explosion is much louder than the humming of a bee, both sounds travel with equal speed.

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

The extension in a string obeying Hooke's law $v$ is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5\ x$, the speed of sound will be

  1. $1.22\ v$
  2. $0.61\ v$
  3. $1.50\ v$
  4. $0.75\ v$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed of sound in stretched string
$v = \dfrac {\overline {T}}{\mu} ..... (i)$
where $T$ is the tension in the string and $\mu$ is mass per unit length.
According to Hooke's law, $F\propto X$
$\therefore T\propto X$ .... (ii)
From Eqs. (i) and (ii)
$v\propto$
$\therefore v' = \overline {1.5V} = 1.22\ V$.

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

According to Newton's formula, the speed of sound in air at STP is:
(Take the mass of $1$ mole of are is $29 \times 10^{-3} \,\,kg)$

  1. $250 \,\, m \,\,s^{-1}$
  2. $260 \,\, m \,\,s^{-1}$
  3. $270 \,\, m \,\,s^{-1}$
  4. $280 \,\, m \,\,s^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1$ mole of any gas occupies $22.4$ liters at STP.
Therefore, the density of air at STP is
$\rho = \dfrac{\text{Mass of one mole of air}}{\text{Volume of one mole of air at STP}}$

$= \dfrac{29 \times 10^{-3} \,\,kg}{22.4 \times 10^{-3} \,\,m^3} = 1.29 \,\,kg \,\,m^{-3}$

At STP, $P = 1\,\,atm = 1.01 \times 10^5 \,\,N \,\,m^{-2}$

$V =\sqrt{\left( \dfrac { P }{ \rho  }\right)}=\sqrt { \dfrac {1.01 \times 10^5 \,\,N \,\,m^{-2}  }{ 1.29 \times kg \,\,m^{-3} }  } = 280 \,\,m \,\,s^{-1} $

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

The speed of sound through a gaseous medium bears a constant ratio with the rms speed of its molecules. What is this constant ratio ?

  1. $\sqrt{\dfrac{\gamma}{3}}$
  2. $\gamma -1$
  3. $\sqrt{\dfrac{2\gamma}{3}}$
  4. $\gamma$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$V _{sound}=\sqrt{\dfrac{\gamma RT}{M}}$ and $V _{rms}=\sqrt{\dfrac{3RT}{M}}$
$\Rightarrow\dfrac{V _{sound}}{V _{rms}}=\sqrt{\dfrac{\gamma}{3}}$
Hence (A) is correct.

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

If $C _{s}$ be the velocity of sound in air and $C$ be the rms velocity, then

  1. $C _{S} < C$
  2. $C _{s}=c$
  3. $C _{s}=C\left(\dfrac {\gamma}{3}\right)^{1/2}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of sound in air, ${{C} _{s}}=\sqrt{\dfrac{\gamma P}{\rho }}\,\ldots \ldots \,(1)$

 $ Where, $

$ \gamma =specific\,heat\,ratio $

$ P=\,pressure $

$ \rho =\,density $

RMS velocity of air molecule, $C=\sqrt{\dfrac{3\overline{R}T}{{{M} _{o}}}}=\sqrt{\dfrac{3P}{\rho }}\,\ldots \ldots \,(2)$

$ where,\, $

$ \overline{R}=\text{universal}\,\text{gas}\,\text{constant} $

$ {{M} _{o}}=Molecular\,mass $

$ T=temperature $

From (1) and (2)

${{C} _{s}}=C{{\left( \dfrac{\gamma }{3} \right)}^{1/2}}$