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 wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A travelling wave tube is given by
$y = \dfrac{0.8}{(3x^2 + 12 xt + 12t^2 + 4)}$, where x and y are in m and t is in s . The velocity of the wave

  1. 3 m/s

  2. 5 m/s

  3. 2 m/s

  4. 7 m/s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} y=\dfrac { { 0.8 } }{ { 3{ x^{ 2 } }+12xt+12{ t^{ 2 } }+4 } }  \ =\dfrac { { 0.8 } }{ { 3\left( { { x^{ 2 } }+4x+4{ t^{ 2 } } } \right) +4 } }  \ =\dfrac { { 0.8 } }{ { 3{ { \left( { x+2t } \right)  }^{ 2 } }+4 } }  \ =\dfrac { { 0.8 } }{ { 3\times 4{ { \left( { \dfrac { x }{ 2 } +t } \right)  }^{ 2 } }+4 } }  \ \therefore Velocity=2m/s \end{array}$

$\therefore $ Option $C$ is correct.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10$ m $s^{-1}$. If the minimum time interval between two instant when the string is flat is $0.5$s, the wavelength of the waves is?

  1. $25$ m
  2. $20$ m
  3. $15$ m
  4. $10$ m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given frequency $f$=$\dfrac { 1 }{ t } $ and velocity $\nu$=10 m/s

We know $\nu =\lambda f\ \lambda =\dfrac { \nu  }{ f } =\dfrac { 10 }{ \frac { 1 }{ 0.5 }  } =5\quad m\ $
Since both the waves are similar but moves in opposite direction its toatl wavelength of the wave will be 10 m

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Mark out the correct statements with respect to wave speed and particle velocity for a transverse travelling mechanical wave on a string.

  1. The wave speed is same for the entire wave, while particle velocity is different for different points at a particular instant.

  2. Wave speed depends upon property of the medium but not on the wave properties.

  3. Wave speed depends upon both the properties of the medium and on the properties of wave.

  4. Particle velocity depends upon properties of the wave and not on medium properties.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave speed v = sqrt(T/mu) depends only on the properties of the medium (tension T and linear density mu). Particle velocity depends on the wave's amplitude and frequency, which are properties of the wave itself.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Two waves $Y _ { 1 } =  { a \sin \omega t }$  and  $Y _ { 2 } = \operatorname { asin } ( \omega t + \delta )$  are producing interference, then resultent intensity is:

  1. $a ^ { 2 } \cos ^ { 2 } \delta / 2$
  2. $2 a ^ { 2 } \cos ^ { 2 } \delta / 2$
  3. $3 a ^ { 2 } \cos ^ { 2 } \delta / 2$
  4. $4 a ^ { 2 } \cos ^ { 2 } \delta / 2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$Y _{1}+Y _{2}=a\sin\omega t+a\sin(\omega t+8)$
$Y=a\left[\sin\omega t+\sin(\omega t+8)\right]$
$Y=a\left[2\sin\left(\dfrac{\omega t+\omega t+8}{2}\right)\cos\left(\dfrac{8}{2}\right)\right]$
$Y=2a\sin\left(\omega t+\dfrac{8}{2}\right)\cos\left(\dfrac{8}{2}\right)$
$Y=\left[2a\cos \left(\dfrac{8}{2}\right)\right]\sin(\omega t+8/2)$
As Intensity $\alpha A^{2}$
Here $I \alpha \left[2a\cos\left(\dfrac{8}{2}\right)\right]^{2}$
$I\alpha 4a^{2}\cos^{2}\left(\dfrac{8}{2}\right)$
Option $D$ is correct.



Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A person observe two points on a string as a travelling wave passes them. The points are at $x _ { 1 } = 0$ and $x _ { 2 } = 1 m.$ The transverse motions of the two points are found to be as follows:
$y _ { 1 } = 0.2 \sin 3 \pi t$
$y _ { 2 } = 0.2 \sin ( 3 \pi t + \pi/8 )$
What is the maximum wavelength?

  1. $32 m$
  2. $16 m$
  3. $8 m$
  4. $4 m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The phase difference delta_phi = k * delta_x. Given y1 = 0.2 sin(3 * pi * t) and y2 = 0.2 sin(3 * pi * t + pi/8), the phase difference is pi/8 for a distance delta_x = 1 m. Thus, k = (pi/8) / 1 = pi/8. Since k = 2 * pi / lambda, we have pi/8 = 2 * pi / lambda, so lambda = 16 m.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a ware is represented by $y = {10^4}\,\sin \,\left[ {100t - \frac{X}{{10}}} \right]$ here $X$ in meter and $t$ in second$.$ The velocity of the wave will be $:-$

  1. $100 m/s$
  2. $250 m/s$
  3. $750 m/s$
  4. $1000 m/s$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The wave equation is y = A sin(omega * t - k * x). Here, omega = 100 and k = 1/10. Wave velocity v = omega / k = 100 / (1/10) = 1000 m/s.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a progressive wave for a wire is: 
$Y=4\sin{\left[\cfrac{\pi}{2}\left(8t-\cfrac{x}{8}\right)\right]}$. If $x$ and $y$ are measured in cm then velocity of wave is :

  1. $64 cm/s$ along $-x$ direction
  2. $32 cm/s$ along $-x$ direction
  3. $32 cm/s$ along $+x$ direction
  4. $64 cm/s$ along $+x$ direction
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\begin{array}{l} w=4\pi  \ K=\dfrac { \pi  }{ { 16 } }  \ v=\dfrac { w }{ K } =64\, m/s\, along\, \, +x-axis \ Hence, \ option\, \, D\, \, is\, correct\, \, answer. \end{array}$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a standing wave in a string fixed at both ends is given as $ y =  A \quad sin \quad  kx \quad cos \quad \omega t $
The amplitude and frequency of a particle vibrating at the mid of an antiode and a node are respectively

  1. $A,\dfrac{\omega }{{2\pi }}$
  2. $\dfrac{A}{{\sqrt 2 }},\dfrac{\omega }{{2\pi }}$
  3. $A,\dfrac{\omega }{{\pi }}$
  4. $\sqrt 2 A,\dfrac{\omega }{{2\pi }}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Which of the following equations represents a transverse wave travelling along -y axis?

  1. $x = A\sin\ (\omega t\ -\ ky)$
  2. $x= A\ sin\ (\omega t\ +\ ky)$
  3. ${ y } _{ 0 }\ =A\sin\ (\omega t - kX )$
  4. ${ y } _{ 0 } = A\ sin (\omega t + kX )$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} For\, \, negative\, \, y-axis \ sign\, \, of\, \, \omega t\, \, & \, \, ky\, \, should\, \, be\, \, same\,  \ x=A\sin  \left( { \omega t+ky } \right)  \ Hence, \ option\, \, B\, \, is\, correct\, \, naswer. \end{array}$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The $(x, y)$ co-ordinates of the corners of a square plate are $(0, 0) (L, 0) (L, L)$ & $(0, L)$. The edges of the plate are clamped & transverse standing waves are set up in it. If $u (x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time, the possible expression(s) for $u$ is/are : ($a$ = positive constant) 

  1. $a\displaystyle \cos \left(\dfrac{\pi x}{2 L}\right)$ $\displaystyle \cos \left(\dfrac{\pi y}{2 L}\right)$
  2. $a\displaystyle \sin \left(\dfrac{\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{\pi y}{L}\right)$
  3. $a\displaystyle \sin \left(\dfrac{\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{2\pi y}{L}\right)$
  4. $a\displaystyle \cos \left(\dfrac{2\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{\pi y}{L}\right)$
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation
The expression for $u(x,y)$ should satisfy the following conditions-
i) $u=0$ at $x=0$ and at $y=0$
ii) $u=0$ at $x=L$ and at $y=L$
Only choices B and C satisfy this condition.
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The displacement of the particle at $x=0$ of a stretched string carrying wave in the positive x-direction is given $f(t)=A sin \frac {t} {T})$. The wave speed is V. Write the wave equation 

  1. $f(x,t)=A sin (\frac {t} {T}) - (\frac{x} {V})$
  2. $f(x,t)=A sin (\frac {t} {T}) + (\frac{x} {VT})$
  3. $f(x,t)=A sin (t+- (\frac{x} {V})$
  4. $f(x,t)=A sin (\frac {t} {T}) - (\frac{x} {VT})$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a wave traveling in the positive x-direction, the function is f(t - x/v). Given f(t) = A sin(t/T), the wave equation is f(x, t) = A sin((t - x/v) / T) = A sin(t/T - x/(vT)).

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A uniform string of length $L$ fixed between the two ends is vibrating in three segments. The wavelength of wave in string is

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

$\begin{array}{l} \dfrac { { 3\lambda  } }{ 2 } =L \ \lambda =\dfrac { { 2l } }{ 3 }  \end{array}$

$\therefore $ Option $C$ is correct.