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 spectra the electromagnetic spectrum electromagnetic spectrum electromagnetic waves

An electromagnetic wave has a frequency of $500MHz$ and a wavelength of $60cm$. Calculate the velocity of the wave.

  1. $3\times 10^8kms^{-1}$
  2. $3\times 10^8cms^{-1}$
  3. $3\times 10^{-8}ms^{-1}$
  4. $3\times 10^8ms^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The formula for velocity, when given wavelength and the frequency of the wave, is written as: $v=f\lambda $.
In this formula, $f$ represents frequency, $v$ represents the velocity of the wave, and $\lambda $ represents the wavelength of the wave.  
Here, the frequency of the wave is $500 MHz = 500000000 Hz$  and the wavelength is $60 cm = 0.6 m$
Hence, the velocity of the wave is $3\times { 10 }^{ 8 }m/s$.

Multiple choice physics fluid pressure pressure in air introduction to atmospheric pressure pressure exerted by air devices to measure pressure

If the intensity of the incident radio wave of  $1\mathrm { w } / \mathrm { w } ^ { 2 }$  is reflected by the surface, find the pressure exerted on the surface?

  1. $5.67 \times 10 ^ { - 9 } N / m ^ { 2 }$
  2. $6.67 \times 10 ^ { - 9 } N / m ^ { 2 }$
  3. $8.67 \times 10 ^ { - 9 } N / m ^ { 2 }$
  4. $9.67 \times 10 ^ { - 8 } \mathrm { N } / \mathrm { m } ^ { 2 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For reflecting surface, Pressure

$\begin{array}{l} =\frac { { 2F } }{ C }  \ =\frac { { 2\times 1 } }{ { 3\times { { 10 }^{ 8 } } } } =6.67\times { 10^{ -9 } }N/{ m^{ 2 } } \ Ans.\, \, (B) \end{array}$

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
C Correct answer
Explanation

Rewriting the cosine wave as a sine wave with a phase shift, y_2 becomes A_0 sin(omega t - kx + pi/6 + pi/2) = A_0 sin(omega t - kx + 2pi/3). The phase difference between the two waves is 2pi/3 radians (120 degrees). Using the vector addition formula for amplitudes with equal component amplitudes A_0, the resultant amplitude is A_0.

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.