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

The displacement of particles in a string stretched in the $X-$ direction is represented by $y$. Among the following expressions for $y$, those describing wave motion are:

  1. $\cos { Kx } \sin { \omega t }$
  2. $-a\cos { \left( Kx-\omega t \right) }$
  3. $-a\cos { \left( Kx+\omega t \right) }$
  4. $-a\sin { \left( Kx-\omega t \right) }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A wave moving with constant speed on a uniform string passes the point $x = 0$ with amplitude $\displaystyle A _{0}$, angular frequency $\displaystyle \omega _{0}$ and average rate of energy transfer $\displaystyle P _{0}$. As the wave travels down the string it gradually loses energy and at the point x = $\displaystyle l $, the average rate of energy transfer becomes $\displaystyle \dfrac{P _{0}}{2}$. At the point x = $\displaystyle l$, angular frequency and amplitude are respectively

  1. $\displaystyle \omega _{0}$ and $A _{0}/\sqrt{2}$
  2. $\displaystyle \omega _{0}/\sqrt{2}$ and $A _{0}$
  3. less than $\displaystyle \omega _{0}$ and $A _{0}$
  4. $\displaystyle \omega _{0}/\sqrt{2}$ and $ A _{0}/\sqrt{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average power of a wave is proportional to the square of the amplitude and the square of the frequency. If the frequency remains constant as the wave travels, the reduction in power must be due to a reduction in amplitude.

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

A stationary wave $y=0.4\sin \cfrac{2\pi}{40}x\cos 100\pi t$ is produced in a rod fixed at both end. The minimum possible length of the rod is given by:

  1. 10 m
  2. $20\sqrt2m$

  3. 20 m

  4. 28 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a standing wave y = A sin(kx) cos(omega*t), the nodes occur where sin(kx) = 0. For a rod fixed at both ends, the length L must be an integer multiple of half-wavelengths. Given k = 2*pi / 40, lambda = 40. Minimum length is lambda / 2 = 20.

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

Two strings A and B with $\mu= 2 \ kg/m$ and $\mu= 8 \ kg/m$ respectively are joined in series and kept on a horizontal table with both the ends fixed. The tension in the string is 200 N. If a pulse of  amplitude 1 cm travels in A towards the junction, then find the amplitude of reflected and transmitted pulse. 

  1. $A _r=2 A _T=7$
  2. $A _r=\dfrac{-1}{3} A _T=\dfrac{2}{3}$
  3. $A _r=8 A _T=9$
  4. $A _r=3 A _t=4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of wave in string A, ${v _A} = \sqrt {\dfrac{T}{{{\mu _A}}}}  = \sqrt {\frac{{200}}{2}}  = 10\,\,m/s$

Velocity of wave in string B,${v _B} = \sqrt {\dfrac{T}{{{\mu _B}}}}  = \sqrt {\frac{{200}}{8}}  = 5\,\,m/s$
Using $k = \dfrac{w}{v} \Rightarrow {k _A} = 0.1w\,\,and\,{k _B} = 0.2w$
Amplitude of reflected pulse, ${A _B} = \dfrac{{{k _A} - {k _B}}}{{{k _A} + {k _B}}}A = \dfrac{{0.1 - 0.2}}{{0.1 + 0.2}} \times 1 =  - \dfrac{1}{3}$
Amplitude of transmitted pulse,${A _T} = A - \left| {{A _R}} \right| = 1 - \dfrac{1}{3} = \dfrac{2}{3}\,\,cm$

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

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

  1. $Y = 0.8 A sin(Kx - \omega \ t + 30^o + 180^o)$
  2. $Y = 0.8 A sin(Kx + \omega \ t + 30^o + 180^o)$
  3. $Y = 0.8 A sin(Kx + \omega \ t - 30^o)$
  4. $Y = 0.8 A sin(Kx + \omega$t + 30^o)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a wave reflects from a denser medium, it undergoes a phase change of 180 degrees. The amplitude of the reflected wave is determined by the energy reflection coefficient (R = sqrt(0.64) = 0.8).

Multiple choice physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

A transverse wave propagating along x-axis isrepresented by
$y\left (x, t \right ) = 8.0 \sin \left (0.5 \pi x - 4 \pi rt - \frac{\pi} {4}  \right )$
where $x$ is in metres and t is in seconds. The speed of the wave is:-

  1. $4 \pi$ m/s
  2. $0.5 \pi$ m/s
  3. $\frac{\pi} {4}$ m/s

  4. 8 m/s
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$V$ = $\frac{\omega} {k}$ = $\frac{4\pi} {0.5 \pi}$ = $8ms^{-1}$

Multiple choice physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

A monochromatic plane wave of speed c and wavelength $\lambda$ is diffracted at a small aperture. The diagram illustrates successive wave fronts.
After what time will some portion of the wave front GH reach point P?

  1. $\dfrac{3\lambda}{2c}$
  2. $\dfrac{2\lambda}{c}$
  3. $\dfrac{3\lambda}{c}$
  4. $\dfrac{4\lambda}{c}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The distance between two consecutive lines(wavefronts ) ia $\lambda$.
So, wavefront XY is separated by a distance of 3λ from the wavefront that has reached point P.

Distance that needs to be travelled = $3\lambda$
Speed of light = $c$

Speed =$\dfrac{Distance}{time}$
Time = $\dfrac{Distance}{Speed}$
        = $\dfrac{3\lambda}{c}$