Tag: waves

Quizzes (32) Questions (233)

Questions Related to waves

Multiple choice energy in wave motion oscillation and waves waves physics

With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the direction of propagation are

  1. Energy, momentum and mass

  2. Mass and momentum

  3. Energy and mass

  4. Energy and momentum
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Whenever any wave travels through a material medium, the particles of the medium start vibrating about their mean positions.

Every vibrating particle transfers its vibration to its immediate next particle.
In any vibration there exists Kinetic Energy and Potential Energy. As the vibration gets transfered, the energy also gets transfered.
Momentum is defined as the product of mass and velocity. Since the particles have mass and they are in motion, they have momentum. So obviously when vibration is transfered, momentum is also transfered.
In any wave motion, the vibration travels in the forward direction, but no particle actually travels forward. Hence mass doesn't get transfered.
We get an illusion that something is moving forward, although nothing moves forward.

Please note that the question is about a longitudinal wave, then also these same facts are applicable to a transverse wave also.

Multiple choice energy in wave motion oscillation and waves waves physics

The amplitude of two waves are in ratio 5 : 2. If all other conditions for the two waves are same, then what is the ratio of their energy densities?

  1. 5 : 2

  2. 5 : 4

  3. 4 : 5

  4. 25 : 4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Energy density of wave is given by
$u=2\pi^2n^2pA^2$
or $u \propto A^2$   (As n and p are constant)
$\therefore \dfrac{u _1}{u _2}=\dfrac{A _1^2}{A _2^2}=\dfrac{5^2}{2^2}$
So, $u _1:u _2=25:4$

Multiple choice energy in wave motion oscillation and waves waves physics

A progressive wave on a string having linear mass density $\rho$ is represented by $y = A\sin \left (\dfrac {2\pi}{\lambda} x - \omega t\right )$ where $y$ is in $10\ mm$. Find the total kinetic energy (in $\mu l)$ passing through origin from $t = 0$ to $t = \dfrac {\pi}{2\omega}$.
[Take : $\rho = 3\times 10^{-2} kg/ m; A = 1mm; \omega = 100\ rad/ sec; \lambda = 16\ cm]$

  1. $6$
  2. $7$
  3. $8$
  4. $9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The kinetic energy passing through a point is calculated by integrating the power or using the energy density formula. Given the parameters, the calculation leads to 9.

Multiple choice energy in wave motion oscillation and waves waves physics

A clamped string is oscillating in nth harmonic, then 

  1. total energy of oscillations will be $n^{2}$ times that of fundamental frequency
  2. total energy of oscillations will be $(n-1)^{2}$ times that of fundamental frequency

  3. average kinetic energy of the string over a complete oscillations is half of the total energy of the string

  4. none of these
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

For a sine wave, $y = A \sin(kx -  \Omega  t)$
Velocity equation for this wave is $V _y =  \Omega A \cos(kx - \Omega  t)$
Kinetic energy = $ d(KE) = 1/2(V _y^2 \times dm) = 1/2(V _y^2 \times  \mu  dx)$, $ \mu $ is the linear mass density.


=> $1/2( \mu  \times  \Omega ^2 \times A^2 \times cos^2(kx -  \Omega  t)) dx$
integrating at $t = 0,$ with limits as $0$ and $ \lambda $, we have

$K.E = 1/4( \mu \times \Omega^2 \times A^2 \times  \lambda $)
Potential energy, $dU = 1/2 (  \Omega  ^2 \times y^2 \times  \mu ) dx $

integrating at $t = 0$, with limits as $0$ and $ \lambda $, we have
$U = 1/4( \mu \times \Omega  ^2 \times A^2 \times  \lambda $)

Total energy $E = K.E + U
$
=> $E = 1/2( \mu  A^2  \lambda $)
Therefore, for the first and fundamental frequency, energy is 
$E _1 = (1/2( \mu  A^2  \lambda ))/n^2$
And clearly from the above derivation, we have, K.E is half the total energy.

Multiple choice energy in wave motion oscillation and waves waves physics

To determine the position of a point like object precisely ______ light should be used.

  1. polarized

  2. short wavelength

  3. long wavelength

  4. intense
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
To determine the position of a point like object precisely light of short wavelength should be used.

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}}}$