Physics

Wave Motion

489 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 standing waves waves physics

A traveling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and  

  1. The wavelength is 5 m

  2. The frequency is 5 Hz

  3. The velocity of propagation is 5 m/s

  4. The wavelength is 0.2 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The frequency is $5Hz$


Phase difference,

$\Delta \phi =\dfrac{2\pi}{T}(\Delta t)$

$2\pi =\dfrac{2\pi}{T}(0.2)$

$\Rightarrow \dfrac{1}{T}=5 sec^{-1}$

$n=5Hz$

Multiple choice standing waves waves physics

The equation of a traveling and stationary wave are ${ y } _{ 1 }=a sin(\omega t-kx)$ and ${ y } _{ 2 }=a \sin kx  \cos \omega t$. The phase difference between two point ${ x } _{ 1 }=\dfrac { \pi  }{ 4k }$ and $ { x } _{ 2 }=\dfrac { 4\pi  }{ 3k } $ are ${ \phi  } _{ 1 }$ and ${ \phi  } _{ 2 }$ respectively for two waves where k is the wave number, the ratio of ${ \phi  } _{ 1 }/{ \phi  } _{ 2 }$ 

  1. 6/7

  2. 16/3

  3. 12/13

  4. 13/12
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice standing waves waves physics

A standing wave pattern is formed on a string. One of the waves is given by equation  $Y _ { 1 } a \cos ( \omega t - K X + \pi / 3 )$  then the equation of the other wave such at  $X = 0$  a noode is formal

  1. $y _{ 2 } = \operatorname { a sin } \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  2. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  3. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 2 \pi } { 3 } \right)$
  4. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 4 \pi } { 3 } \right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a standing wave formed by two waves y1 and y2, if a node exists at x=0, the resultant wave must be zero at x=0 for all t. This requires y1 + y2 = 0 at x=0. Given y1 = a cos(wt - kx + pi/3), at x=0, y1 = a cos(wt + pi/3). Thus, y2 must be -a cos(wt + kx + pi/3), which is equivalent to a cos(wt + kx + pi/3 + pi) = a cos(wt + kx + 4pi/3).

Multiple choice standing waves waves physics

Two simple harmonic waves of amplitude 5 cm and 3 cm and of the same frequency travelling with the same speed in opposite directions superpose to produce stationary waves. The ration of the amplitude at a node to that at an antinode in the resultant wave is

  1. zero

  2. infinity

  3. 5:3

  4. 1:4
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice standing waves waves physics

The equation of stationary wave is given by $y=5\, cos (\pi x/3)\, sin 40 \pi t$ where y and x are given in cm and time t in second. Then a node occurs at the following distance 

  1. 3 cm

  2. 10 cm

  3. 5 cm

  4. 1.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Nodes occur where the spatial part of the stationary wave equation equals zero, meaning cos(pi x / 3) = 0. This happens when pi x / 3 = pi/2, 3pi/2, etc., which yields x = 1.5 cm for the first node. Thus, 1.5 cm is the correct position for a node.

Multiple choice standing waves waves physics

A wave represented by $y=2 cos (4x-\pi t)$ is superposed with another wave to form a stationary wave such that the point x= 0 is a node. The equation of other wave is:

  1. $2 sin(4x+\pi t)$
  2. $-2 cos (4x -\pi t)$
  3. $-2 cos (4x +\pi t)$
  4. $-2 sin (4x -\pi t)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to options

If $y _2=-2\cos(4x+\pi t)$
Then, when superimposed,
$y=y _1+y _2\ \quad 2\cos(4x-\pi t)-2\cos(4x+\pi t)\ =2[2\sin(\cfrac{(4x-\pi t)+(4x+\pi t)}{2})\sin(\cfrac{(4x-\pi t)-(4x+\pi t)}{2})]\ \quad=2[2\sin(4x)\sin(-\pi t)]\y=-4\sin(4x)\sin(\pi t)$
at $y=0\Rightarrow y=0$ (i.e node)

Multiple choice physics beats in sound waves

Two waves $\mathrm{y} _{1}=\mathrm{A}\cos(0.5\pi \mathrm{x}-100\pi \mathrm{t})$
and $\mathrm{y} _{2}=\mathrm{A}\cos(0.46\pi \mathrm{x}-92\pi \mathrm{t})$ are travelling in a pipe placed along $\mathrm{x}$-axis. Find the number of times intensity is maximum in time interval of 1 sec.

  1. 4

  2. 6

  3. 8

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

Beat frequency$=|f _1-f _2|=(50-46)=4s^{-1}$

One beat frequency consists of a maximum and a minimum
So the number of maxima are ${f}=4$

Multiple choice physics range of hearing sound: production of sound audible, infrasonic and ultrasonic sounds different sounds


A microwave and an ultrasonic sound wave have the same wavelength. Their frequencies are in the ratio (approximately) 

  1. $10^2$
  2. $10^4$
  3. $10^6$
  4. $10^8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Frequency of microwaves, $\upsilon _m \approx 10^{11}Hz$
Frequency of ultrasonic sound waves,$\upsilon _m \approx 10^5Hz$
$\therefore \, \dfrac{\upsilon _m}{\upsilon _u} = \dfrac{10^{11}}{10^{5}} = 10^6$

Multiple choice physics range of hearing sound: production of sound audible, infrasonic and ultrasonic sounds different sounds

Ultrasonic, intrasonic and audible waves travel through a medium with speeds $V _u,V _i,$ and $V _a$ respectively, then (given constant temperature)

  1. $V _i=V _a=V _u$
  2. $V _u>V _a>V _i$
  3. $V _u < V _a < V _i $
  4. ${ V } _{ a }\le { V } _{ u }={ V } _{ i }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The speed of sound in a medium depends on the properties of the medium (density, elasticity) and temperature, not on the frequency of the sound wave.

Multiple choice

How is a wavelength measured?

  1. The length of one wave to the next wave cm2

  2. The distance of the top of one wave to the top of the next.

  3. By the duration of time it takes to travel back

  4. The distance from the center outwards
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A wavelength is defined as the physical distance between two consecutive corresponding points on a wave, such as from crest to crest or trough to trough.

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

Two waves are approaching each other with a velocity of $16\, m/s$ and frequency $n$. the distance between two consecutive nodes is 

  1. $\dfrac{16}{n}$
  2. $\dfrac{8}{n}$
  3. $\dfrac{n}{16}$
  4. $\dfrac{n}{8}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The wavelength lambda is given by velocity divided by frequency, so lambda = 16 / n. The distance between two consecutive nodes in a standing wave is equal to half of the wavelength, which is lambda / 2 = 8 / n.

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

Two waves of wavelengths 99 cm and 100 cm both travelling with velocity 396 m/s are made of interfere. The number of beats produced by them per second are

  1. $1$
  2. $2$
  3. $4$
  4. $8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} Velocity\, \, of\, \, wave\, \, V=n\lambda  \ Where\, \, n=frequency\, \, of\, \, wave\, \,  \ \Rightarrow n=\frac { v }{ \lambda  }  \ { n _{ 2 } }=\frac { { { v _{ 2 } } } }{ { { \lambda _{ 2 } } } } =\frac { { 396 } }{ { 100\times { { 10 }^{ -2 } } } } =396Hz \ no.\, \, of\, \, beats\, \, ={ n _{ 1 } }-n _2\, =4 \end{array}$

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).