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

 Standing waves are generated on string laded with a cylindrical body. If the cylinder immersed in water, the length of the loops changes by a factor of 2.2. The specific gravity of the material of the cylinder is 

  1. 1.11

  2. 2.15

  3. 2.50

  4. 1.26
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The frequency of a vibrating string is proportional to the square root of tension. When immersed in water, the tension changes due to the buoyant force. The ratio of frequencies (or loop lengths) relates to the density of the object and the fluid, leading to the specific gravity calculation.

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

In a string the speed of wave is 10 m/s and its frequency is 100 Hz . The value of the phase difference at a distance 2.5 cm will be :

  1. ${ \pi }/{ 2 }$
  2. ${ \pi }/{ 8 }$
  3. ${ 3\pi }/{ 2 }$
  4. ${ 2\pi }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed of wave $(v) = 10 m/s$

Frequecy$(\gamma)=100Hz$
Wavelength$(\lambda)=\dfrac{10}{100}=\dfrac{1}{10}ms$
$2\pi$ phase is covered in $\dfrac{1}{10}m$
Hence, at distance of 2.5 m, the phase is $\dfrac{2\pi \times 0.025}{0.1}=\dfrac{\pi}{2}$



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

A travelling wave travelled in string in +x direction with 2 cm/s, particle at x=0 oscillates according to equation y (in mm) $= 2\sin { \left( \pi t+{ \pi  }/{ 3 } \right)  }$. What will be the slope of the wave at x=3 cm and t=1 s

  1. $-\sqrt { 3 } { \pi }/{ 2 }$
  2. $\tan ^{ -1 }{ \left( -\sqrt { 3 } { \pi }/{ 2 } \right) }$
  3. $-\sqrt { 3 } { \pi }/{ 20 }$
  4. $-\sqrt { 3 } { \pi }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The wave equation is y = 2 sin(pi * t - pi * x / v + pi / 3) where v = 2 cm/s. The slope is the partial derivative dy/dx. Calculating dy/dx at x=3 and t=1 yields the negative value of the derivative component.

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

The wave-function for a certain standing wave on a string fixed at born ends is y(x, t) = 0.5 sin (0.025$\pi$x) 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
A Correct answer
Explanation
$\phi \vec { B } .\vec { dl } ={ \mu  } _{ 0 }{ I } _{ enclosed }$.
Inside the hollow pipe, ${ I } _{ enclosed }=0$.
$\therefore$   $\phi \vec { B } .\vec { dl } =0$
$\Rightarrow$  $B=0$ inside the pipe $\longrightarrow \left( A \right) $.
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A uniform wire of length 20 m and weighing 5 kg hangs vertically. If g=10 $ms^{-2}$, then the speed of transverse waves in the middle of the wire is

  1. $10 ms ^{-1}$
  2. $10\sqrt2 ms ^{-1}$
  3. $15ms ^{-1}$
  4. $2 ms ^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

$m=5kg$
$l=20m$
$\mu=\dfrac{m}{l}=\dfrac{5}{20}=0.25kg/m$
$g=10m/s^2$
Tension in the middle of the wire, $T=\dfrac{m}{2}g$
$T=\dfrac{5}{2}\times 10=25N$
Velocity, $v=\sqrt{\dfrac{T}{\mu}}$
$T=\sqrt{\dfrac{25}{0.25}}=10m/s$
The correct option is A.

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 = $\dfrac{Distance}{Speed}$
        = $\dfrac{3\lambda}{c}$
Multiple choice difference between interference and diffraction explaining wave phenomena diffraction

If the intensity of the waves observed by two coherent sources is $I$. Then the intensity if resultant wave in constructive interference will be:-

  1. $2 I$
  2. $4 I$
  3. $I$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

During constructive interference, the amplitude of the resultant wave is the sum of the individual amplitudes (a + a = 2a). Since intensity is proportional to the square of the amplitude, the resultant intensity becomes (2a)^2 = 4a^2 = 4I.

Multiple choice difference between interference and diffraction explaining wave phenomena diffraction

In the case of interference, The maximum and minimum intensities are in the ratio $16:9$. Then

  1. The maximum and minimum amplitude will be in the ratio 9:5

  2. The intensities of the individual waves will be in the ratio 4:3.

  3. The amplitudes of the individual waves will be in the ratio 4:1

  4. None of the above is true
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given I_max / I_min = 16 / 9, the ratio of amplitudes a_1 / a_2 can be found since I proportional to a^2. Taking square roots gives (a_1 + a_2) / (a_1 - a_2) = 4 / 3, which solves to a_1 / a_2 = 7:1. Since the options given do not match this correct calculation, the right choice is none of the above.