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

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 Hz$. The mass of the wire is $3.5 \times 10^{-2}kg$ and its linear mass density is $4.0 \times 10^{-2} kgm^{-1}$. What is the speed of a transverse wave on the wire?

  1. $69 \ ms^{-1}$
  2. $79 \ ms^{-1}$
  3. $89 \ ms^{-1}$
  4. $99 \ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a wire vibrating in its fundamental mode, the frequency f = v / (2L). However, we can use the relation v = sqrt(T/mu). Given the mass M = 0.035 kg and linear density mu = 0.04 kg/m, the length L = M/mu = 0.875 m. The fundamental frequency f = v / (2L) = 45 Hz, so v = 45 * 2 * 0.875 = 78.75 m/s, which rounds to 79 m/s.

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 $x _2 = 1m$. 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 frequency in Hertz?

  1. $1.5 Hz$
  2. $3 Hz$
  3. $4.5 Hz$
  4. $1 Hz$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The transverse motion is given by y = A sin(omega * t + phi). Comparing y1 = 0.2 sin(3 * pi * t) with the standard form, omega = 3 * pi. Since omega = 2 * pi * f, we have 3 * pi = 2 * pi * f, which gives f = 1.5 Hz.

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

The equation of wave in string is $\displaystyle y = 20\sin \frac{\pi x}{2} \cos 40\pi t$ in metre. The speed of the wave is 

  1. $Zero$
  2. $80\, m/s$
  3. $320\, m/s$
  4. $160\, m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\large \begin{array}{l} Here, \ y=20\sin  \frac { { \pi x } }{ 2 } \cos  40\pi t-----(i) \ compare\, with\, eqution,\, (i)\,  \ \Rightarrow y=2r\, \, \sin  \frac { { 2\pi  } }{ \lambda  } \, \times \, \, \cos  \frac { { 2\pi  } }{ \lambda  } Vt \ Now, \ \Rightarrow \frac { { 2\pi  } }{ \lambda  } =\frac { \pi  }{ 2 } \, \, and\, \, \frac { { 2\pi  } }{ \lambda  } V=40\pi  \ so, \ \Rightarrow \frac { \pi  }{ 2 } \, \times V=40\pi  \ \therefore \, \, V=80\, m/s \end{array}$

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

A 100 Hz sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of $3.5\, \times\, 10^{-3}\, kg/m$ and a tension of 35 N. At time t = 0, the point x = 0, has maximum displacement in the positive y direction. Next when this point has zero displacement the slope of the string is $\pi /20$. which of the following expression represent (s) the displacement of string as a function of x (in metre) and t (in second).

  1. $y\, =\, 0.025\, cos\, (200 \pi t\, -\, 2 \pi x)$
  2. $y\, =\, 0.5\, cos\, (200 \pi t\, -\, 2 \pi x)$
  3. $y\, =\, 0.025\, cos\, (100 \pi t\, -\, 10 \pi x)$
  4. $y\, =\, 0.5\, cos\, (100 \pi t\, -\, 10 \pi x)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the wave have the form $y=Asin(\omega t-kx+\phi)$
Since the frequency is $100Hz$, $\omega=2\pi\nu=200\pi$
Speed of the wave=$\sqrt{\dfrac{T}{\mu}}=\dfrac{\omega}{k}$
$\implies k=2\pi$
Since displacement is maximum at (x,t)=(0,0), $sin(0+0+\phi)=1$
$\implies \phi=\dfrac{\pi}{2}$
Thus the wave is $y=Acos(\omega t-kx)$
$Slope=\left|\dfrac{dy}{dx}\right|=Aksin(\omega t-kx)=\dfrac{\pi}{20}$ at $(x,t)=(0,0)$
Thus $Ak=\dfrac{\pi}{20}$
$\implies A=0.025m$
Thus the correct answer is option A.
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Which of the following statements is correct?

  1. Longitudinal waves consist of crests and troughs

  2. In case of transverse waves, the particles of the medium vibrate at right angles to the direction of wave

  3. Transverse waves are produced when a tuning fork is struck in air

  4. Longitudinal waves are produced when a stone is dropped on the surface of water in a pond
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Answer is C.

A transverse wave is a wave in which the medium vibrates at right angles to the direction that the wave travels. An example of a transverse wave is a wave in a rope held with a hand on one end and tied to a pole on another end.
In this wave, energy is provided by a persons hand moving one end of the rope up and down. The direction of the wave is down the length of the rope away from the persons hand. The rope itself moves up and down as the wave passes through it.
The characteristic described in statement c is a property of all transverse waves, but not necessarily of all mechanical waves. A mechanical wave can also be longitudinal.
Hence, option C is correct and rest of the statements are incorrect.

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

A travelling wave on a string is given by $y=A\ \sin [\alpha x+\beta t+\dfrac {\pi}{6}]$. The displacment oscillation of a point $\alpha=0.56\ /cm,\beta=12/sec,A=7.5\ cm,x=1\ cm$ and $t=1s$ is

  1. $4.6\ cm,46.5\ cms^{1}$
  2. $3.75\ cm,77.94\ cms^{1}$
  3. $1.76\ cm,7.5\ cms^{1}$
  4. $7.5\ cm,75\ cms^{1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given y = A sin(alpha x + beta t + pi/6). The displacement is y = 7.5 sin(0.56 * 1 + 12 * 1 + pi/6) = 7.5 sin(0.56 + 12 + 0.5236) = 7.5 sin(13.08) in radians, which calculates to approx 3.75 cm. The particle velocity is the time derivative of displacement, v = dy/dt = A beta cos(alpha x + beta t + pi/6) = 7.5 * 12 * cos(...) = 90 * cos(...) = 77.94 cm/s.

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
B Correct answer
Explanation

For a standing wave y = A sin(kx) cos(omega t), the amplitude of a particle at position x is A_particle = |A sin(kx)|. A point midway between a node and an antinode corresponds to kx = pi/4. At this point, the amplitude is A * sin(pi/4) = A / sqrt(2). The frequency of vibration of any particle in a standing wave is the same as the wave frequency, which is omega / (2 pi).

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

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