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

A form of modulation in which the amplitude of a carrier wave is varied in accordance with some characteristic of the modulating signal is known as

  1. Attenuation

  2. Amplitude modulation

  3. Modem

  4. Multiplexer

  5. Distortion
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is the correct option. A form of modulation in which the amplitude of the carrier wave is varied in accordance with some characteristic of the modulating signal, is known as amplitude modulation.

Multiple choice

Directions: For the Assertion (A) and Reason (R) below, choose the correct alternative from the following. Assertion: When velocity is kept constant and wavelength is halved, then the frequency is doubled. Reason: Velocity = frequency  wavelength.

  1. Both A and R are true and R is the correct explanation of A.

  2. Both A and R are true but R is not the correct explanation of A.

  3. A is true but R is false.

  4. A is false but R is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Both A and R are true, and R is the reason for A. Hence, option (1) is correct.

Multiple choice physics wave motion reflection of waves

The equation of a stationary wave is $Y=10\sin{\cfrac{\pi x}{4}}\cos{20\pi t}$. The distance between two consecutive nodes in meters is -

  1. 4

  2. 2

  3. 5

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Y = 10\sin \dfrac{{\pi x}}{4}\cos \pi t$

At nodles amplitude part is zero.
$\begin{array}{l} \Rightarrow 10\sin  \dfrac { { \pi x } }{ 4 } =0 \ \Rightarrow \dfrac { { \pi x } }{ 4 } =0,\pi ,2\pi  \ \Rightarrow x=0.x=4,x=8 \end{array}$
$\therefore 4$  is distance between two consultative node.
$\therefore$ Option $A$ is correct.

Multiple choice physics wave motion reflection of waves

The phase change between incident and reflected sound wave from a free end is

  1. $0$
  2. $\pi $
  3. $3\pi $
  4. $2\pi $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

At a free and, the wave is reflected as it is with just as change in its direction of propagation 
$y= A  \sin  ( \omega t+kx)$
$y _r= A  \sin  (\omega t-kx)$
phase difference in time domain $= 0$

Multiple choice physics wave motion reflection of waves

What characteristics of a point on the string will you use to find the location of the antinode

  1. displacement

  2. velocity

  3. wavelength

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

An antinode is a point on the string, where the amplitude at that point is maximum 

The correct option is (a)

Multiple choice physics wave motion reflection of waves

The equation of a progressive wave is given by $y=10 sin (5t-x)$. The wave gets reflected from a open boundary. The equation of the reflected wave is

  1. $y=10 sin (5t-x)$
  2. $y=-10 sin (5t-x)$
  3. $y=10 sin (5t+x)$
  4. $y=10 sin (5t+x+\pi)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In reflection of a wave at open boundaries, the phase reversal dosent take place

The correct option is (c)

Multiple choice physics wave motion reflection of waves

A wave of frequency $100$ Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of $10$ cm from the fixed end of the string. The speeds of incident(and reflected) waves are?

  1. $5$ $cms^{-1}$
  2. $10$ $cms^{-1}$
  3. $20$ $cms^{-1}$
  4. $40$ $cms^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given frequency $\nu$=100 H. 

Also distance between two successive nodes$=>\dfrac { \lambda  }{ 2 } =10\ \lambda =20\quad cm$
And we know $\nu =n\lambda \ n=\frac { \nu  }{ \lambda  } =\dfrac { 100 }{ 20 } =5\quad cm/s$

Multiple choice physics wave motion reflection of waves

A composition string is made up by joining two strings of different masses per unit length $\longrightarrow \mu $ and $4\mu.$ The composite string is under the same tension. A transverse wave pulse : $Y=(6 mm) \sin (5t+40x)$, where '$t$' is in seconds and '$x$' in meters, is sent along the lighter string towards the joint. The joint is at $x=0.$ The equation of the wave pulse reflected from the joint is 

  1. $(2 mm) \sin(5t-40x)$
  2. $(4 mm) \sin(40x-5t)$
  3. $- (2 mm) \sin(5t-40x)$
  4. $(2 mm) \sin(5t-10x)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the wave is travelling from low to more dense medium, thus there will be inversion of the reflected wave . Since it travels back from origin, thus $40x$ will become $-40x.$ Also, amplitude of reflected wave is given by:
${ A } _{ r }=\dfrac { Z _{ 1 }-{ Z } _{ 2 } }{ { Z } _{ 1 }+Z _{ 2 } } A.\quad Z=\mu c=\mu \sqrt { \dfrac { T }{ \mu  }  } =\sqrt { \mu T } \ Thus\quad { A } _{ r }=\dfrac { \sqrt { \mu T } -\sqrt { 4\mu T }  }{ \sqrt { \mu T } +\sqrt { 4\mu T }  } A=\dfrac { -1 }{ 3 } A\ $
Thus it become $-6/3=-2$.

Multiple choice physics wave motion reflection of waves

Which of the following statement is incorrect superposition of waves?
(i) After superposition frequency,wavelength and velocity of resultant wave remains same
 (ii) After superposition amplitude of resultant wave is equal to amplitude of either wave 
 (iii) Mechanical wave cannot superposed with electromagnetic wave
 (iv) For superposition two waves should have equal wavelength,frequency and amplitude

  1. I & III Only

  2. I & II Only

  3. I,II, & III Only

  4. II & IV Only
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (i) is incorrect because the resultant wave's amplitude changes, though frequency/wavelength remain the same. Statement (iii) is incorrect because mechanical and electromagnetic waves can superpose (e.g., light interacting with a medium). Statement (ii) is incorrect as the resultant amplitude depends on phase. Statement (iv) is incorrect as superposition occurs for waves of different properties. Given the options, (i) and (iii) are the most clearly incorrect statements regarding the fundamental principles of superposition.

Multiple choice physics wave motion reflection of waves

A wave travels on a light string. The equation of the waves is $Y\, = \,A\, sin\,(kx\,-\,\omega\,t+\,30^{\circ})$. It is reflected from a heavy string tied to end of the light string at x = 0 . If 64% of the incident energy is reflected then the equation of the reflected wave is  

  1. $Y\, =\,0.8 \,A\, sin\,(kx\,-\,\omega\,t\,+\,30^{\circ}\,+\,180^{\circ})$
  2. $Y\, =\,0.8 \,A\, sin\,(kx\,+\,\omega\,t\,+\,30^{\circ}\,+\,180^{\circ})$
  3. $Y\, =\,0.8 \,A\, sin\,(kx\,-\,\omega\,t\,-\,30^{\circ})$
  4. $Y\, =\,0.8 \,A\, sin\,(kx\,-\,\omega\,t\,+\,30^{\circ})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are three things we need to take into account:

  • Energy transfer
  • Change in velocity
  • Change in phase
We know that power delivered is proportional to $A^{2}$
Hence if power(energy) reduces to 64%. We get that Amplitude must reduce to 80% or 0.8A.
Now the reflected wave is moving in the opposite direction. (velocity is negative now).
Also because of the hard soft boundary reflection (there is a phase lag of $180^{\circ}$
Hence the new equation becomes:
$y = 0.8A sin(kx + \omega t + 30^{\circ} + 180^{\circ})$
Hence option B.

Multiple choice physics wave motion reflection of waves

A pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with :

  1. a phase change of ${180}^{o}$ with velocity reversed

  2. the same phase as the incident pulse with no reversal of velocity
  3. a phase change of ${180}^{o}$ with no reversal of velocity

  4. the same phase as the incident pulse but with velocity reversed
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A pulse of wave train when travels along a stretched string and reaches the fixed end of the string, then it will be reflected back to the same medium and the reflected ray suffers a phase change of $\pi$ with the incident wave but wave velocity after reflection reverses its direction.