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 problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

When a transverse plane wave traverses a medium, individual particles execute periodic motion given by the equation  $y=0.25\cos(2\pi t-\pi x)$. The phase difference for two positions of same particle which are occupied by time intervals $0.4 second$ apart is

  1. $144^{o}$
  2. $135^{o}$
  3. $72^{o}$
  4. $108^{o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\omega =\dfrac{2\pi}{T}$
$T=\dfrac{2\pi}{\omega}$
$T=1sec$
$\therefore 2\pi \ rad \ in \   1 sec$
$in \ 0.4 sec \  2\pi\times 0.9$
$=144^o$

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Reflection of a light wave at a fixed point results in a phase difference between incident and reflected wave of

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

Reflections of light at the interface between media often produce phase differences. The phase difference between incident and reflected wave is $2\pi$ and $\pi / 2$ radians.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The phase difference between two waves represented by 
${y _1} = {10^{ - 6}}\sin \left[ {100t + \frac{x}{{50}} + 0.5} \right]m$
${y _2} = {10^{ - 6}}\cos \left[ {100t + \frac{x}{{50}}} \right]m$
where x is expressed in metres and t is expressed in seconds is approximately

  1. 1.07 rad

  2. 2.07 rad

  3. 0.5 rad

  4. 1.5 rad
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$y _{1}=10^{-6} \sin \left[100 t + \dfrac{x}{50}+ 0.5\right] m$
$y _{2}=10^{-6} \cos \left[100 t + \dfrac{x}{50}\right] m$
So,$y^{1}=10^{-6} \cos\left[\dfrac{\pi}{2}-\left(100 t + \dfrac{x}{50}+0.5\right)\right]$
$y^{1}=10^{-6} \cos \left[\dfrac{-\pi}{2}+100 t+\dfrac{x}{50}+0.5\right]$
$\triangle \phi =\phi _{2}-\phi _{1}$
$\phi _{2}=0$ where as $\phi _{1}=0.5-\dfrac{\pi}{2}$
So,
$\triangle \phi=\phi _{2}-\phi _{1}=\dfrac{\pi}{2}-0.5=1.07 \ rad$
option $-A$ is correct.

































Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Two waves of the same amplitude and frequency arrive at a point simultaneously. what should the phase difference between the waves so that amplitude of the resultant wave is double(2A) 

  1. $\dfrac {\pi}{2} radian$
  2. $\dfrac {2\pi}{3} radian$
  3. $\dfrac {3\pi}{4} radian$

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

Resultant amplitude A_res = sqrt(A1^2 + A2^2 + 2 * A1 * A2 * cos(phi)). For A1 = A2 = A, A_res = 2 * A * cos(phi / 2). For A_res = 2 * A, cos(phi / 2) = 1, so phi / 2 = 0, which means phi = 0.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A travelling wave has a velocity of 400 m/s and has a wavelength of 0.5 m. What is the phase difference between two points in the wave that are 1.25 milli secs apart

  1. $2 \pi$
  2. $2 \pi/3$
  3. $2 \pi/5$
  4. $ \pi/6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The frequency of the wave is $f = v/\lambda=400/0.5=800 Hz$

Time period = 1/800 = 1.25 ms

Thus, both the points are one time period apart. Hence their phase difference will be zero or $2 \pi$

The correct option is (a)

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Two waves of frequencies 20 Hz and 30 Hz travels out from a common point. The phase difference between them after 0.6 sec is

  1. $12\pi $
  2. ${\pi \over 2}$
  3. $\pi $
  4. ${{3\pi } \over 4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Beats period$=\cfrac{1}{30-20}=0.1second\ \Delta Y=\cfrac{2\pi}{T}\Delta t\ \quad=\cfrac{2\pi}{0.1}\times0.6=2\pi\times6=12\pi\ \therefore\Delta Y=12\pi$

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A progressive wave of wavelength 5 cm moves along +X axis. What is the phase difference between two points on the wave separated by a distance of 3 cm at any instant

  1. $3 \pi/5$
  2. $6 \pi/5$
  3. $2 \pi/5$
  4. $7 \pi/5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Phase difference = $(2\pi/5)$ path difference $\implies$ phase difference = $6 \pi/5$

The correct option is (b) 

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The phase difference between two waves, represented by ${ y } _{ 1 }={ 10 }^{ -6 }\sin { \left[ 100t+\left( x/50 \right) +0.5 \right]\ m } $ and ${ y } _{ 2 }={ 10 }^{ -6 }\cos { \left[ 100t+\left( x/50 \right)  \right]\ m } $. Where $x$ is expressed in metre and $t$ is expressed in seconds, is approximately

  1. $1.07\ radian$
  2. $2.07\ radian$
  3. $0.5\ radian$
  4. $1.5\ radian$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

In a string the speed of wave is $10m/s$ and its frequency is $100$ Hz. The value of the phase difference at a distance $2.5$cm will be :

  1. $\pi/2$
  2. $\pi/8$
  3. $3\pi/2$
  4. $4\pi$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,


$f=100Hz$


$x=2.5cm$

$v=10m/s$  path difference

wavelength, $\lambda =\dfrac{v}{f}=\dfrac{10}{100}=0.1m$

The phase difference, $\phi=\dfrac{2\pi}{\lambda}\times x$

$\phi=\dfrac{2\pi}{0.1}\times 2.5\times 10^{-2}$

$\phi=\dfrac{\pi}{2}$

The correct option is A.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A transverse progressive wave on a stretched string has a velocity of $10ms^{-1}$ and frequency of $100Hz$. The phase difference between two particles of the string which nbare $2.5cm$ apart will be :

  1. $\cfrac{\pi}{8}$
  2. $\cfrac{\pi}{4}$
  3. $\cfrac{3\pi}{8}$
  4. $\cfrac{\pi}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,


$v=10m/s$ velocity


$f=100Hz$ frequency

$\Delta=2.5cm$ path difference

wavelength, $\lambda=\dfrac{v}{f}$

$\lambda=\dfrac{10}{100}=0.1m$

Phase difference,

$\phi=\dfrac{2\pi}{\lambda}\times \Delta$

$\phi=\dfrac{2\pi}{0.1}\times 2.5\times 10^{-2}$

$\phi=\dfrac{\pi}{2}$

The correct option is D.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The distance between two consecutive crests in a wave train produced in string is 5 m. If two complete waves pass through any point per second, the velocity of wave is:

  1. $2.5 \mathrm { m } / \mathrm { s }$
  2. $5 \mathrm { m } / \mathrm { s }$
  3. $10 \mathrm { m } / \mathrm { s }$
  4. $15 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,

Two consecutive crest =$5\,m$.

Two wave cross in time, $t=\,1\sec $

Wavelength = distance between two consecutive crest

$\lambda =5\,m$

Velocity, $v=\dfrac{2\lambda }{t}=\dfrac{2\times 5}{1}=10\,m{{s}^{-1}}$

Hence, wave speed is $10\,m{{s}^{-1}}$

 

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Two waves $E _ { 1 } = E _ { 0 } \sin \omega t$  and $E _ { 2 } = E _ { 0 } \sin ( \omega t + 60 )$ superimpose each other. Find out initial phase of resultant wave?

  1. $30 ^ { \circ }$
  2. $60 ^ { \circ }$
  3. $120 ^ { \circ }$
  4. $0 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the resultant wave be 
$E=E0' \sin (wt+\phi)$./ Then 
$E=E _1+E _2$
$E=E _0\sin wt +E _0\sin (wt+60^o)$
$E=E _0(\sin wt +\sin (wt +60^o)$
As $\sin \cos +\sin (B)=2\sin \left (\dfrac {A+B}{2}\right) \cos \left (\dfrac {B-A}{2}\right) $
$\sin wt +\sin (wt +60^o)=2 \sin (wt +30^o).\cos (wt)$
So, $E=2E _0 \cos (wt) \sin (wt+30^o)$
So, $E _0=2E _0 \cos wt $ and $ \phi =30^o$
Option $A$ is correct


Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 0.5 $\pi $ the wave velocity is

  1. 144 ${ ms }^{ -1 }$
  2. 384 ${ ms }^{ -1 }$
  3. 256 ${ ms }^{ -1 }$
  4. 720 ${ ms }^{ -1 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Phase difference is related to path difference by delta phi = (2pi / lambda) * delta x. Given delta phi = 0.5 pi and delta x = 0.8 m, we find lambda = 3.2 m. Wave velocity v = frequency * wavelength = 120 * 3.2 = 384 ms^-1.