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 the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

If $\vec{E} = E _0 \cos (kz) \cos (\omega t)\hat{i}$ then $\vec{B}$ for electromagnetic wave is:

  1. $\vec{B} = \dfrac{E _0}{C} \hat{k}$
  2. $\vec{B} = \dfrac{E _0}{C} \sin (kz) \sin (\omega t)\hat{i}$
  3. $\vec{B} = \dfrac{E _0}{C} \sin (kz) \cos (\omega t) \hat{j}$
  4. $\vec{B} = \dfrac{E _0}{C} \cos (kz) \sin (\omega t) \hat{j}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{dE}{dz} = -\dfrac{dB}{dt}$
If $\vec{E} = E _0 \, \cos (kz) \cos (\omega t)$ then
$\vec{B} = \dfrac{E _0}{C} \sin (kz) \sin (\omega t)$ will satisfy the equation

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

For the propagation of electromagnetic waves

  1. Medium is required

  2. no medium is required

  3. E and B are in mutually opposite phase

  4. E and b do not contriute
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Electromagnetic waves are a result of changing electric field creating magnetic field and the magnetic field does the same for electric field. Unlike mechanical waves, electromagnetic waves does not require material medium to transfer energy from one place to another.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

In a stationary wave, 

  1. Phase is same at all points in a loop

  2. Amplitude is same at all points

  3. Energy is constant at all points

  4. Temperature is same at all points
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let two waves be $y _1=A \sin\ (wt-kx)$
$y _2=A \sin\ (wt+kx)$
$y=y _1+y _2$
$=(2A \cos\ kx)\sin\ wt.$ 
For all point in one loop i.e as $x$ varies in $2A \cos k x$, the phase is same. The phase changes only after crossing a node.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

Equation of a standing wave is expressed as $y=2A\sin { \omega t } \cos { kx } $. In the equation, quantity $\omega /k$ represents 

  1. $the\ transverse\ speed\ of\ the\ particles\ of\ the\ string.$
  2. $the\ speed\ of\ the\ component\ waves.$
  3. $the\ speed\ of\ the\ standing\ wave.$
  4. $a\ quantity\ that\ is\ independent\ of\ the\ properties\ of\ the\ string.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equ of standing wave is $y=2A \sin wt \cos Kx$. The quantity $\dfrac { W }{ K } $ always represent the speed of the wave.


Hence Option (C) is correct.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

Energy is not carried by

  1. transverse progressive wave

  2. longitudinal progressive wave

  3. transverse stationary wave

  4. electromagnetic wave
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The main difference between stationary and progressive waves is: Progressive waves transfer energy from one place to another, without transferring matter and Stationary waves do not transfer energy from one place to another. Clearly only one option has stationary waves.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

Mark incorrect Statement 

  1. Magnitude of strain is maximum at antinode because medium particles at antinodes have maximum possible velocity

  2. Nodes and antinodes form in case of stationary waves only.

  3. In case of stationary waves maximum pressure change occurs at antinode.
  4. Due to propagation of longitudinal wave in air maximum pressure change is equal to $\dfrac{2\pi fs _{0}}{\rho v}.$ ($f$ : frequency, $s _{0}$ : maximum displacement, $\rho$ : density of medium, $v $: speed of wave)
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

(A) Magnitude of strain is maximum at antinode because medium particles at antinodes have minimum possible velocity.
(B) Nodes and antinodes form in case of travelling waves also.
(C) In case of stationary waves maximum pressure change occurs at node.
(D) Due to propagation of longitudinal wave in air maximum pressure change is equal to $2\pi f s _{0}\rho V$.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

In a standing wave on a string.

  1. In one time period all the particles are simultaneously at rest twice.

  2. All the particles must be at their positive extremes simultaneously once in one time period.

  3. All the particles may be at their positive extremes simultaneously once in a time period.

  4. All the particles are never at rest simultaneously.
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Standing waves are obtained when two waves with same angular frequencies and velocity are superimposed, (They are however moving in the opposite directions).
$x(t) = A\sin(\omega t - kx) + A\sin(\omega t + kx + \delta)$
$x(t) = 2A\cos(kx)\sin(\omega t +\dfrac{\delta}{2})$
For all particles to be simultaneously at rest, the value of the sine function must be equal to zero.
i.e. $\omega t + \dfrac{\delta}{2} = n\pi$
$\Rightarrow$ $t = \dfrac{1}{\omega}(n\pi - \dfrac{\delta}{2})$
$\omega = \dfrac{2\pi}{T}$
$\Rightarrow$ $t = \dfrac{T}{2\pi}(n\pi - \dfrac{\delta}{2})$
$t _{1} =  \dfrac{T}{2\pi}(n\pi - \dfrac{\delta}{2})$
$t _{2} =  \dfrac{T}{2\pi}((n+1)\pi - \dfrac{\delta}{2})$
$t _{2} - t _{1} = \dfrac{T}{2}$


So, the time between this event happening twice is half to time period, so in one cycle this would happen twice. So Option (A)
For the particle to be at positive extreme the sine function can take a value of 1 only.
It can be shown that this happens at an interval of '$T$'
So it will happen twice in a time period if the displacement is max at the start of the time period and once more at the end of the time period,
or else it would happen only once in a time period. Hence Option (C)

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

Equation of a standing wave is expressed as y = 2A sin$\omega$t coskx. In the equation, quantity $\omega$/k represents

  1. the transverse speed of the particles of the string.

  2. the speed of the component waves

  3. the speed of the standing wave.

  4. a quantity that is independent of the properties of the string.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$y=1A\sin\omega t\cos kx\k=\cfrac{2\pi}{\lambda}\ \Rightarrow \cfrac{\omega}{K}=\cfrac{\omega\times \lambda}{2\pi}=\cfrac{\lambda}{2\pi/\omega}=\cfrac{\lambda}{T}=\lambda f=V$

$\Rightarrow\cfrac{\omega}{K}=$ Velocity of wave particles (transverse speed)

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

The speed of mechanical waves depends on :-

  1. Density of medium

  2. Elasticity of medium

  3. Elasticity and density of medium

  4. Frequency of the wave.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The speed of a mechanical wave in a medium is determined by the medium's elastic properties (which provide the restoring force) and its inertial properties (density). Both factors are essential for wave propagation.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

A suspension bridge is to be built across valley where it is known that the wind can gust at $5\ s$ intervals. It is estimated that the speed of transverse waves along the span of the bridge would be $400\ m/s$. The danger of reasonant motions in the bridge at its fundamental frequency would be greater if the span had a length of :

  1. $2000\ m$
  2. $1000\ m$
  3. $400\ m$
  4. $80\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Resonance occurs when the driving frequency matches the natural frequency of the system. For a bridge span, the fundamental frequency is f = v / (2L). Given v = 400 m/s and a period of 5s (frequency f = 0.2 Hz), setting 0.2 = 400 / (2L) leads to 0.4L = 400, so L = 1000 m.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

The wave-function for a certain standing wave on a string fixed at both ends is $y\left( x,t \right) =0.5\sin { \left( 0.025\pi x \right)  } \cos { 500\ t } $ where $x$ and $y$ are in centimeters and t is in seconds. The shortest possible length of the string is: 

  1. $126\ cm$
  2. $160\ cm$
  3. $40\ cm$
  4. $80\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the shortest possible length, it should be allowing fundamental frequency resonance.

In fundamental frequency
$L=\dfrac { \lambda  }{ 2 } \quad \quad \quad \quad \left( \because K=\dfrac { 2\pi  }{ \lambda  }  \right) $
$=\dfrac { 2\pi /K }{ 2 } =\dfrac { \pi  }{ K } $
from $y=0.5\sin\left( 0.025\pi x \right) \cos\left( 500t \right) $
$K=0.025\pi \quad \quad \quad (on\quad comparing\quad with\quad y=A\sin\left( Kx \right) \cos\left( wt \right) )$
$\therefore \quad L=\dfrac { \pi  }{ 0.025\pi  } =\dfrac { 1000 }{ 25 } $
$\left[ L=40cm \right] $

Hence Option (C) is correct.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

If the difference between the frequencies of two waves is 10 Hz then time interval between successive maximum intensity is:

  1. $10 s$
  2. $1 s$
  3. $0.1 s$
  4. $0.01 s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The beat frequency is the difference between the frequencies of two waves. The time interval between successive maximum intensities (beats) is the reciprocal of the beat frequency: T = 1/10 = 0.1 s.