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 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

Two waves are represented by the equations $y _{1}a sin (\omega t+kx+0.57)m$ $y _{2}a cos (\omega t+kx)m$  
where x in meter and t in Sec.  the phase difference between them is 

  1. 0.57 radian

  2. 1.0 radian

  3. 1.25 radian

  4. 1.57 radian
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convert y2 to sine form: y2 = a sin(omega*t + kx + pi/2). The phase of y1 is omega*t + kx + 0.57. The phase of y2 is omega*t + kx + 1.57. The difference is 1.57 - 0.57 = 1.0 radian.

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

Consider the wave represented by $y=\cos(500t-70x)$ where $x$ is in metres and $t$ in seconds. the two nearest points in the same phase have a separation of 

  1. $2\pi/7\ m$
  2. $2\pi/7\ cm$
  3. $20\pi/7\ m$
  4. $20\pi/7\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the same phase, the path difference must be a multiple of the wavelength. Here, k = 70, so 2pi/lambda = 70, lambda = 2pi/70 m = 2pi/70 * 100 cm = 20pi/7 cm.

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

Four waves are expressed as
(i) $y _ { 1 } = a _ { 1 } \sin \omega t$                                            (ii) $y _ { 2 } = a _ { 2 } \sin 2 \omega t$
(iii) $y _ { 3 } = a _ { 3 } \cos \omega t$                                         (iv) $y _ { 4 } = a _ { 4 } \sin ( \omega t + \phi )$
The interference is possible between

  1. (i) and (iii)

  2. (i) and (ii)

  3. (ii) and (iv)

  4. Not possible at all
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
For interference frequency should be same.
Ans. (A)