Physics

Wave Motion

536 Questions

Wave motion questions cover the principles of traveling and stationary waves, including their equations and intensities. The topics explore interference patterns, phase differences, and electromagnetic radiation speeds. Mastery of these concepts is vital for physics sections in engineering and civil services examinations.

Wave interferenceStanding wavesPhase differenceElectromagnetic radiationWave equations

Wave Motion Questions

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

The equation, $Y=0.02 sin (500 \pi t) cos(4.5x)$ represents

  1. progressive wave of frequency 250 Hz along x-axis

  2. a stationary wave of wavelength 1.4 m

  3. a transverse progressive wave of amplitude 0.02 m
  4. progressive wave of speed of about $350ms^{-1} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Comparing the given wave equation with standard standing wave equation
$y (x, t) = A \sin (\omega t)\cos (kx)$, 


we get, $k =4.5$

$k = \dfrac{2\pi}{\lambda}$

$\Rightarrow \lambda = \dfrac{2\pi}{k} =1.4$ $m$

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

The equation of a progressive wave is $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$ where x is in metre and t is in second. The velocity of the wave is

  1. $100\pi\,m/s$
  2. $50\pi\,m/s$
  3. $25\pi\,m/s$
  4. $\pi\,m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of the progressive wave is given as, $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$.

The velocity of the wave would be equal to

$\dfrac{\omega}{k}=\dfrac{4\pi}{0.04}=100\pi\;m/s$

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

Which of the following statements are correct?

  1. A wave front is a locus of points vibratig in same phase

  2. Wavelength is separation between two consecutive points vibrating in same phase

  3. For two sources to be coherent their frequencies must be same

  4. All of the above statements are correct.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A wavefront is indeed a locus of points in the same phase. Wavelength is the distance between consecutive points in the same phase. Coherent sources must have the same frequency and constant phase difference.

Multiple choice energy in wave motion oscillation and waves waves physics

If the energy density and velocity of a wave are $u$ and $c$ respectively then the energy propagating per second per unit area will be

  1. $u/c$
  2. $c^2u$
  3. $uc$
  4. $c/u$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the energy density and velocity of a wave are $u$ and $c$ respectively then the energy propagating per second per unit area will be $uc.$

Multiple choice energy in wave motion oscillation and waves waves physics

The kinetic energy per unit length for a wave on a string is the positional coordinate

  1. True

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

The kinetic energy for a particle is given by $(\mu \Delta x/ 2) (\dfrac{dy}{dt})^2$

Thus, it depends only on the time variable and not on the position variable

Multiple choice energy in wave motion oscillation and waves waves physics

A travelling wave has an equation of the form $A(x,t)=f(x+vt)$. The relation connecting positional derivative with time derivative of the function is:

  1. $\dfrac{dA}{dt}=\pm v^2 \dfrac {dA}{dx}$
  2. $\dfrac{dA}{dt}=\pm v \dfrac {dA}{dx}$
  3. $\dfrac{dA}{dt}=\pm \sqrt(v) \dfrac {dA}{dx}$
  4. $\dfrac{dA}{dt}=(2 \pi v/\lambda) \dfrac {dA}{dx}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Positional derivative and time derivative of a function f is $\dfrac{dA}{dt}=\pm v \dfrac {dA}{dx}$

The correct option is (b)

Multiple choice energy in wave motion oscillation and waves waves physics

The total energy per unit length for a travelling wave in a string of mass density $\mu$ , whose wave function is $A(x,t) = f(x \pm vt)$ is given by: 

  1. $E _tot = \sqrt(\mu/2) (\dfrac{dA}{dt})^2$
  2. $E _tot = (\mu/2) (\dfrac{dA}{dt})^2$
  3. $E _tot = (\mu/2)^2 (\dfrac{dA}{dt})^2$
  4. $E _tot = (2\mu) (\dfrac{dA}{dt})^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a travelling wave y = f(x - vt), the energy density is related to the square of the partial derivative of the wave function with respect to time, specifically (mu/2) * (dy/dt)^2.

Multiple choice energy in wave motion oscillation and waves waves physics

Potential energy of a string depends on 

  1. Wave velocity

  2. Amplitude of the wave

  3. Extent of stretching of the string

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Potential energy of a string depends on the extent of stretching.

The correct option is (c)

Multiple choice energy in wave motion oscillation and waves waves physics

If the frequency and amplitude of a transverse wave on a string are both doubled, then the amount of energy transmitted through the string is

  1. doubled

  2. become 4 time

  3. becomes 16 times

  4. becomes 32 times
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Energy transmitted through the string $E  \propto  \nu^2  A^2$

Now, $\nu' = 2  \nu                      A' = 2  A$
Thus, $\dfrac{E'}{E}  = \dfrac{(\nu')^2  (A')^2}{\nu^2    A^2} = \dfrac{4  \nu^2  \times  4  A^2}{\nu^2   A^2}$

$\implies    E' = 16    E$

Multiple choice energy in wave motion oscillation and waves waves physics

$y _1 = 88\, sin(\omega t - kx)$ and $y _2 = 6 sin(\omega t + kx)$ are two waves travelling in a string of area of cross-section $s$ and density $\rho$. These two waves are superimposed to produce a standing wave. Find the total amount of energy crossing through a node per second.

  1. $\displaystyle \frac{2\rho\omega^{3}s}{k}$
  2. $\displaystyle \frac{3\rho\omega^{3}s}{k}$
  3. $\displaystyle \frac{5\rho\omega^{3}s}{k}$
  4. $\displaystyle \frac{6\rho\omega^{3}s}{k}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 Here, we will take ,

               $y=y _1 + y _2$
                     = $8sin(\omega t-kx) +6 sin(\omega t+kx)$..........(1)
Now, add and subtract $6sin(\omega t -kx)$ in (1).
                      = $8sin(\omega t-kx) +6sin(\omega t+kx) +6sin(\omega t-kx) -6 sin(\omega t
-kx)$
                      =$2sin(\omega t-kx) +12 sin\omega t cos kx$............(2)
We obtained (2) by solving using trigonometric relations.
energy crossing through node per second = power
                       $P=\dfrac{1}{2}\rho \omega^2 (2)^2 Sv$..................(3)
Now, put $v=\dfrac{\omega}{k}$ in eqn. (3)

  We get , $P= \dfrac{2\rho\omega^3 s}{k}$


Multiple choice energy in wave motion oscillation and waves waves physics

Choose the correct alternative(s) regarding standing waves in a string

  1. particles near the antinode have lesser potential energy than the particles near the node when they reaches at its extreme position

  2. All the particles crosses their mean position simultaneously

  3. Energy and momentum can transmitted through node

  4. Particles near the antinode have lesser kinetic energy than the particles near the node when they crosses their mean position
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

At the antinode, the tension and hence the elongation in the string in minimum and hence minimum potential energy. While at the nodes, tension is maximum and hence maximum potential energy. All particles perform SHM with same time period and hence since the phase differecnce between any two particles is constant, they cross mean position simultaneously. 

As note is always at rest, energy and momentum cannot be transferred through it.
Particles at antinode have maximum velocity and hence maximum kinetic energy while crossing the mean position.

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 physics study of sound determination of speed of sound by echo problems on sound sound needs a medium

A sound wave of wavelength $\lambda$ travels towards the right horizontally with a velocity V. It strikes and reflects from a vertical plane surface, travelling at a speed v towards the left. The number of positive crests striking during a time interval of three seconds on the wall is :

  1. $3(V+v)/\lambda$
  2. $3(V-v)/\lambda$
  3. $(V+v)/3\lambda$
  4. $(V-v)/3\lambda$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative velocity of the wave crests with respect to the wall is (V+v). The distance covered by the crests in time t is (V+v)t. The number of crests is distance / wavelength = (V+v)t / lambda. For t=3s, this is 3(V+v)/lambda.