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 sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

Which is true for a wave ? (here n = frequency, T = time period)

  1. nT$=1$
  2. $\displaystyle\frac{n}{T}=2$

  3. n=T

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Frequency is , number of vibrations per (one) second , and time period is the time taken to complete one vibration .

      Let a vibrating body completes n vibrations in 1 s ,
therefore time taken to complete one vibration , $T=(1/n)$ second
  therefore we have , $T=1/n$ ,

            or                  $nT=1$

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

A transverse wave of frequency 50 Hz is reflected from a wall. 50% of the energy of the wave is lost at the wall. The frequency of the reflected wave will be

  1. 25 Hz

  2. 50 Hz

  3. 100 Hz

  4. 75 Hz
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Loss in energy only implies loss in amplitude and not in frequency. Since frequency is a characteristic of the source

The correct option is (b)

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

Two sound waves having pressure
$P _{1}=2 \times 10^{4} \sin (2\pi \times 10^{4}\ t)Pa$ and 
$P _{2}=4 \times 10^{4} \sin (3\pi \times 10^{4}\ t+\pi /6)Pa$
superimpose with each other. Find the amplitude of resultant wave.

  1. $4.47\times 10^{4}\ Pa$
  2. $4.47\ Pa$
  3. $5.67\times 10^{4}\ Pa$
  4. $5.67\ Pa$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The resultant amplitude of two waves with different frequencies is not a simple sum. However, if interpreting as phasors or peak pressure values, the maximum resultant amplitude is sqrt(P1^2 + P2^2 + 2*P1*P2*cos(phi)). With P1=2e4, P2=4e4, and phase difference, the calculation yields approximately 4.47e4 Pa.

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

The time taken by a particle in reaching from a trough to its next crest in a transverse wave is

  1. T/4

  2. T/2

  3. T

  4. 3T/4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A crest and a trough are separated by a distance of $\lambda/2$. A distance of $\lambda/2$ corresponds to a time difference of T/2

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

On the superposition of the two waves given as $y _1=A _0 \sin (\omega t-kx)$ and $y _2=A _0\cos \left(\omega t-kx+\dfrac{\pi}{6}\right) $the resultant amplitude of oscillations will be 

  1. $\sqrt{3}A _0$
  2. $\dfrac{A _0}{2}$
  3. $A _0$
  4. $\dfrac{3}{2}A _0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

Select proper wave equation which describes simple harmonic progressive wave travelling along positive $X$ axis.

  1. $y = A \sin ( \alpha t + k x )$
  2. $y = A \cos ( o t + k x )$
  3. $y = A \sin ( a t - k x )$
  4. $y = - 4 \tan ( \alpha x - k x )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A progressive wave traveling in the positive x-direction is represented by a function of (wt - kx).

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

Sea water at frequency $\nu \  =\  4\  x\  { 10 }^{ 8 }$ Hz has permittivity $\varepsilon  \  \approx \  80\  { \varepsilon   } _{ 0 }$, permeability $\mu \  \approx \  { \mu  } _{ 0 }$ and resistivity $\rho \  =\  0.25\  \Omega m$. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source V(t) = ${ V } _{ 0 }\  \sin { \  (2\pi \nu t) }$. The of amplitude of the displacement current density to the conduction current density is

  1. $\dfrac { 2 }{ 3 }$
  2. $\dfrac { 4 }{ 9 }$
  3. $\dfrac { 9 }{ 4 }$

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Suppose distance between the parallel plates is $D$ and applied voltage $V _{(t)} = V _02\pi vt$.

thus electric field
$E = \dfrac{V _0}{d} \sin (2\pi vt)$
Now using Ohm's law 
$J _c = \dfrac{1}{\phi} \dfrac{V _0}{d}\sin (2\pi vt)$

$\dfrac{V _0}{\phi d}\sin  (2 \pi vt) = J _0^c \sin  2 \pi vt$

Here $J _0^c = \dfrac{V _0}{pd}$
Now the displacement current density is given as
$Jd = \in \dfrac{\delta E}{dt} =\dfrac{\in \delta}{dt}$    $\left[\dfrac{V _0}{dt} \sin (2\pi vt)\right]$

$= \dfrac{\in 2\pi v V _0}{d} \cos (2\pi vt)$

$\Rightarrow = J^d _0 \cos (2\pi vt)$

Where $J _0^d = \dfrac{2\pi V\in V _0}{d}$

$\Rightarrow \dfrac{J^d _0}{J^c _0} = \dfrac{2\pi v \in V _0}{d}. \dfrac{pd}{V _0} = 2\pi v \in \rho$

$= 2\pi \times 80\in _0v\times 0.25 = 4\pi \in _0v \times 10$ 

$= \dfrac{10v}{9\times 10^9} = \dfrac{4}{9}$

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

For a string clamped at both its ends, which of the following wave equation is/are valid for a stationary wave set up in it? (Origin is at one end of string).

  1. $y=A\sin kx.\sin \omega t$
  2. $y=A\cos kx \sin \omega t$
  3. $y=A\sin kx. \cos \omega t$
  4. $y=A\cos kx \cos \omega t$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

For all values of t, y$=0$ at $x=0$
Hence, (A) and (C) are correct.

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.