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 superposition of waves-1: interference and beats distinction between interference and beats beats and its applications beats in sound waves

If 2 waves of same frequency and same amplitude on superposition, produce a resultant disturbance of the same amplitude, the waves differ in phase by

  1. $ \dfrac { \pi }{ 3 } $
  2. $ \dfrac { 2\pi }{ 3 } $
  3. $ { \pi } $
  4. $ { 3\pi } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the amplitude of each wave be $A$ i.e.  $A _1 = A _2 = A$
Thus amplitude of resultant wave  $A _R =A$
Using   $A^2 _R =  A _1^2 + A _2^2 + 2A _1A _2 \cos\theta$
$\therefore$  $A^2 =  A^2 + A^2 + 2A^2 \cos\theta$
Or  $\cos\theta = -0.5$
$\implies  \ \theta = \dfrac{2\pi}{3}$

Multiple choice evs magic with mirrors image of an extended object formed by a plane mirror reflection at plane surface introduction to light and mirror

On reflection from a rigid body, the wave undergoes a phase change of

  1. $90^{\circ}$
  2. $180^{\circ}$
  3. $210^{\circ}$
  4. $120^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a wave reflects off a rigid boundary (a medium with higher optical density or a fixed end), it undergoes a phase shift of 180 degrees (or pi radians).

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

A standing wave is represented by an equation $y= 20 sin (50 \pi t )cos (10 \pi x)$. The frequency of the wave is

  1. 20 Hz

  2. 50 Hz

  3. 25 Hz

  4. 10 Hz
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation of a stationary wave is $y= 2A sin \omega t cos K x$. Comparing this equation with the equation given in the problem, we have
$2 \pi f = 50 \implies f = 25 Hz$

The correct option is (c)

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 statement is incorrect during propagation of plane progressive mechanical wave?

  1. All the particles are vibrating in the same phase.

  2. Amplitude of all the particles is equal.

  3. Particles of the medium executes SHM.

  4. Wave velocity depends upon the nature of the medium.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

During propagation of a plane progressive mechanical wave all the particles are vibrating with different phases.
While all other statement are correct.

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

A standing wave is given by the equation $x=10 sin 5\pi t cos 3 x$. The amplitude of the wave will be

  1. a constant at all times

  2. will be increasing as t increases

  3. will be decreasing as t increases

  4. will fluctuate at x increases
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The amplitude of the stationary wave is $10 cos 3 x$ and this fluctuates as x increases

The correct option is (d)

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

A standing wave is represented by an equation $y= 10 sin 50 \pi t cos 10 \pi x$. The distance between adjacent nodes of the wave is

  1. 0.5 m

  2. 0.2 m

  3. 0.1 m

  4. 0.3 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At nodes, displacement $y=0$

For first node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { \pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { \pi  }{ 2 } \ x=\cfrac { 1 }{ 20 } $
For second node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { 3\pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { 3\pi  }{ 2 } \ x=\cfrac { 3 }{ 20 } $
$\therefore$ distance between them $=\cfrac { 3 }{ 20 } -\cfrac { 1 }{ 20 } \ \quad \quad =\cfrac { 1 }{ 10 } =0.1m$

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 waves in which the particles of the medium travel in the same direction as the waves are

  1. linear waves

  2. longitudinal waves

  3. transverse waves

  4. electromagnetic waves
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The waves in which the displacement of the medium is in the same direction as, or the opposite direction to the direction of the propagation of the wave, are called lognitudinal waves. Ex$:-$ Sound waves, sewmic waves

While $:-$ 
The wave in which the displacement of the medium are at right angles to the direction of propogation, are called trensverse waves.
Ex$:-$ Electromagnetic waves, ripple on water surface.
Option (B) is the correct answer

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 functions represent a traveling wave ?

  1. $({ x-vt })^{ 2 }$
  2. $({ x-vt })^{ 3 }$
  3. ${ 2 }^{ -(x-vt)^{ 2 } }$
  4. ${ e }^{ (x-vt) }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A traveling wave must be a function of (x - vt) or (x + vt). While A, B, and C are functions of (x-vt), they do not satisfy the wave equation (second derivative in x equals 1/v^2 times second derivative in t) for all physical contexts, but e^(x-vt) is a common form for a traveling wave solution.

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 the stationary wave is
$y=2A\quad sin(\cfrac { 2\pi ct }{ \lambda  } )cos(\cfrac { 2\pi x }{ \lambda  } )$
Which of the following statement (s) is wrong?

  1. The unit of ct is same as that of $\lambda$
  2. The unit of x is same as that of $\lambda$
  3. The unit of $2\pi t$ is same as that of $2\pi x/\lambda t$
  4. The unit of $c/\lambda$ is same as that of $x/\lambda$
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

$y=2Asin(\dfrac{2\pi ct}{\lambda}). cos(\dfrac{2\pi x}{\lambda})$


The unit of $\lambda $ and $x$ is $m$


The unit of $ct$ is $m$

The unit of $2\pi t$ is $s$.

The unit of $2\pi x/\lambda t$ is $s^{-1}$

The unit of $\dfrac{c}{\lambda}$ is $s^{-1}$

The unit of $x/\lambda$ is unit less.

The wrong statement is C and D both.

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

In a plane progressive harmonic wave, $V _{P}$ is the maximum particle speed and $V$ is the wave speed. If amplitude of wave is less than $\lambda/ 2\pi$, then

  1. $V = V _{P}$
  2. $V > V _{P}$
  3. $V _{P} < V$

  4. Unpredictable
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Particle speed Vp = A * omega. Wave speed V = omega / k. Vp / V = A * omega / (omega / k) = A * k = A * (2 * pi / lambda). Given A < lambda / (2 * pi), then A * (2 * pi / lambda) < 1, so Vp < V.

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 stationary wave is given by $ y= 5cos \frac { \pi x }{ 3 }  sin 40 \pi t $. where y and x are given cm and time t in second then the amplitude of the progressive wave is

  1. $2.5 cm$
  2. $10 cm$
  3. $5 cm$
  4. $7.5 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The stationary wave equation is y = 2A * cos(kx) * sin(omega * t). Given y = 5 * cos(...) * sin(...), the amplitude of the stationary wave is 5 cm. The amplitude of the component progressive waves is A = 5 / 2 = 2.5 cm.

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 progressive wave travelling along positive direction of x-axis having an amplitude of $0.04\ m$, frequency $440\ Hz$ and wave velocity $330 m/s$ is

  1. $y = 0.04\sin 2\pi \left (440t - \dfrac {4x}{3}\right )$
  2. $y = 0.04\cos 2\pi \left (440t - \dfrac {3x}{4}\right )$
  3. $y = 0.04\sin 2\pi \left (440t + \dfrac {4x}{3}\right )$
  4. $y = 0.04\cos 2\pi \left (440t + \dfrac {4x}{3}\right )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave equation y = A * sin(2 * pi * (ft + x/lambda)) for negative direction or (ft - x/lambda) for positive. Here, positive direction means (ft - x/lambda). f = 440, v = 330, lambda = v/f = 330/440 = 3/4. So 1/lambda = 4/3. Equation: y = 0.04 * sin(2 * pi * (440t - 4x/3)). Note: The option C uses +4x/3 which implies negative direction, but often textbooks use conventions differently. Given the options, C is the closest match.

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

In a stationary wave

  1. Strain is maximum at nodes

  2. amplitude is minimum at nodes

  3. Strain is maximum at antinodes

  4. Amplitude is zero at all points
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a stationary wave, nodes are points where the displacement is always zero, meaning the amplitude is minimum (zero).

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 frequency of plane progressive wave is $100$ Hz. After how much time the same point will be $90^o$ out of phase?

  1. $2.5\times 0^{-3}s$.
  2. $3.5\times 0^{-3}s$.
  3. $4.5\times 0^{-3}s$.
  4. $5.5\times 0^{-3}s$.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$w=2\Pi f$

where f is frequency of wave
Phase angle, $\theta wt$
$90^{\circ}=2\Pi ft$

$t=\dfrac{\Pi }{2\times 2\Pi f}$

$t=\dfrac{1}{4\times 100} $sec

$t=2.5\times 10^{-3}$ sec

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

Progressive wave are waves originating from a source such that they never return to the source.

  1. True

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

progressive waves are waves after generation from the source the keep on propagating on the direction of propagation .

so the answer is A.