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 problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A source oscillates with a frequency 25 Hz and the wave propagates with 300 m/s. Two points A and B are located at distances 10 m and 16 m away from the source. The phase difference between A and B is 

  1. $\displaystyle \frac{\pi}{4}$
  2. $\displaystyle \frac{\pi}{2}$
  3. $\pi$
  4. $2 \pi$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wavelength of the wave=$\lambda=\dfrac{v}{\nu}=\dfrac{300}{25}=12m$

Distance between the two points=$16m-10m=6m=\dfrac{\lambda}{2}$
$=\dfrac{2\pi}{\lambda}\dfrac{\lambda}{2}=\pi$

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

For the travelling harmonic wave  $y(x,t)=2.0 cos $ $ 2\pi $ (10t-0.0080 x+0.35 ) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of $x$

  1. $x=4 m,\ \ \Delta\phi=6.4π \ rad $
  2. $0.5 m,\ \ \ \ \ \Delta\phi=0.6π \, rad $
  3. $ \displaystyle \lambda /2 ,\ \ \ \ \ \ \ \Delta\phi= .6π \ rad$
  4. $ \displaystyle 3\lambda /4,\ \ \ \ \ \Delta\phi= 2.5π \ rad .$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation for a travelling harmonic wave is given as:

$y(x, t)=2.0\,cos\,2\pi(10t-0.0080x+0.35)$
             $=2.0\,cos(20\pi t-0.016\pi x+0.70\pi)$
Where,
Propagation constant, $k = 0.0160\pi$
Amplitude, $a=2\,cm$
Angular frequency, $\omega =20\pi\,rad/s$
Phase difference is given by the relation:
$\phi =kx=2\pi/\lambda$

(a) For $\Delta x=4m= 400 cm$
$\Delta \phi = 0.016\pi\times 400=6.4\pi\, rad$

(b) For $\Delta x=0.5 m = 50 cm$
$\Delta \phi = 0.016\pi \times 50 = 0.8\pi\, rad$

(c) For $\Delta x=\lambda/2$
$\Delta \phi=2\pi/\lambda \times \lambda/2=\pi\, rad$

(d) For $\Delta x=3\lambda/4$
$\Delta \phi=2\pi/\lambda \times 3\lambda/4=1.5\pi\, rad$.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A wave travelling in positive X-direction with A = 0.2 m velocity = 360 m/s and $\lambda$= 60 m, then correct expression for the wave is : -

  1. y = 0.2 sin $\left [ 2\pi (6t+\frac{X}{60}) \right ]$
  2. y = 0.2 sin $\left [\pi (6t+\frac{X}{60}) \right ]$
  3. y = 0.2 sin $\left [ 2\pi (6t-\frac{X}{60}) \right ]$
  4. y = 0.2 sin $\left [\pi (6t-\frac{X}{60}) \right ]$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The general equation for a wave moving in the positive x-direction is y = A sin(2*pi*(ft - x/lambda)). Given A = 0.2, f = velocity/lambda = 360/60 = 6 Hz, and lambda = 60, the equation becomes y = 0.2 sin(2*pi*(6t - x/60)).

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

If two waves, each of intensity ${I} _{0}$, having the same frequency but differing by a constant phase angle of ${60}^{o}$, superpose at a certain point in space, then the intensity of resultant wave is:

  1. $2{I} _{0}$
  2. $\sqrt{3}{I} _{0}$
  3. $3{I} _{0}$
  4. $4{I} _{0}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Resultant intensity for two interfering waves of intensity I_0 and phase difference phi is I = I_1 + I_2 + 2 * sqrt(I_1 * I_2) * cos(phi). With I_1 = I_2 = I_0 and phi = 60 degrees, cos(60) = 1/2, yielding I = I_0 + I_0 + I_0 = 3 I_0.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Equations of a stationary wave and a travelling wave are $y _1=1\,sin(kx)\,cos (\omega t)$ and $y _2=a\,sin\,(\omega t-kx)$.The phase difference between two points $x _1=\dfrac{\pi}{3k}$ and $x _2=\dfrac{3 \pi}{2k}$ is $\phi _1$ for the first wave and $\phi _2$ for the second wave.The ratio $\dfrac{\phi _1}{\phi _2}$ is

  1. 1

  2. 5/6

  3. 3/4

  4. 6/7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Phase difference between two points in a standing wave =$n\pi$

Where n is number of nodes between two points.
Given points are $x _1 = \cfrac{\pi}{3k} = \cfrac{60}{k}$
$x _2 = \cfrac{3\pi}{2k} = \cfrac{210}{k}$
Equation of the standing wave
$ y _1 = a \sin kx \cos \omega t$
At node points $ kx =n\pi$
$ x = \cfrac{n\pi}{k} \quad (n=0,1,2,3...)$
So nodes are =$ \cfrac{\pi}{k} , \cfrac{2\pi}{k} ....$
$ =  \cfrac{180}{k} , \cfrac{360}{k} ....$
Since there is only one node between phase difference  $ \phi _1 = \pi$
For travelling wave $ \phi _2  = \cfrac{2\pi}{\lambda} \triangle x$
From the equation 
$y _2 = a \sin (\omega t - kx)$
$ k = \cfrac{2\pi}{\lambda}$
$ \therefore \phi _2 = k[x _2 - x _1] = k[\cfrac{3\pi}{2k} - \cfrac{\pi}{3k}] = \cfrac{7}{6}\pi$
$ \therefore \cfrac{\phi _1}{\phi _2} = \cfrac{\pi}{\cfrac{7}{6}\pi} = \cfrac{6}{7}$

Multiple choice physics structure of earth seismic waves and tsunami causes of earthquakes origin of earth and its internal energy transfer of charge lightning safety

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $S$ waves is about $4 \,\,km \,\,s^{-1}$ and that of $P$ waves is about $8 \,\,km \,\,s^{-1}$. A seismograph records $P$ and $S$ waves from an earthquake.The first $P$ wave arrives $4$ min before the first $S$ wave. The epicentre of the earthquake is located at a distance of about

  1. $192 km$
  2. $384 km$
  3. $1920 km$
  4. $3840 km$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let $\nu _1, \nu _2$ be speed $S$ of $S$ and $P$ waves and $t _1,t _2$ be the time taken by these waves to travel to reach the seismograph. Let the epicenter of the earthquake is located at a distance $d$ from the seismograph. Then,
$d = V _1 t _1 = V _2 t _2$          ................ .....(i)
Here, $V _1 = 4 km \,\,s^{-1}$ and $V _2 = 8 km \,\,s^{-1}$
$\therefore 4t _1 = 8t _2 \Longrightarrow t _1 = 2t _2$           ....(ii)
and  $t _1 - t _2 = 4 min = 240 s$
$\therefore 2t _2 - t _2 = 240$      ....................  [using (ii)]
or $t _2 = 240 s$
put in Eq. (ii), we get,
$t _1 = 2 \times 240 s = 480 s$
From Eq. (i), we get, $d = (4 km \,\,s^{-1}) (480 s) = 1920 km$
Multiple choice physics structure of earth seismic waves and tsunami causes of earthquakes origin of earth and its internal energy transfer of charge lightning safety

Choose the correct statement.

  1. 'P' waves are slower than 'S' waves.

  2. Both 'P' and 'S' waves have same speed.

  3. 'S' waves are slower than 'P' waves.

  4. None of the above.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The P waves and the S waves are the waves that travel throughout the planet. The P waves are the compression waves that apply force in the direction of propagation whereas the S waves are shear waves that make the medium particle move perpendicular to their direction of motion.
The energy is less easily transmitted in the medium in the case of S waves. So, P waves travel faster.

Option $C$ is correct.
Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

The longitudinal wave can be observed in

  1. Elastic media

  2. inelastic media
  3. Both $(1)$ & $(2)$

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

Longitudinal waves travel only in the elastic medium. These waves comprise of compressions and rarefactions. The speed of Longitudinal waves is given by :

$v=\dfrac{\sqrt{B}}{\rho }$ where B is the bulk modulus of elasticity and $\rho $ is the density of the medium

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

A transverse wave along a string is given by y=$2\sin \left( {2\pi \left( {3t - x} \right) - \frac{\pi }{6}} \right)$, where x and y are in cm and 't' is in second. The acceleration of a particle located at x=4cm at t =1s is 

  1. $36\pi ^2$
  2. $72\pi ^2$
  3. $18\pi ^2$
  4. $12\pi ^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The wave equation is y = 2 sin(6*pi*t - 2*pi*x - pi/6). Velocity v = dy/dt = 2 * 6*pi * cos(6*pi*t - 2*pi*x - pi/6). Acceleration a = dv/dt = -2 * (6*pi)^2 * sin(6*pi*t - 2*pi*x - pi/6). At x=4 and t=1, the argument is 6*pi - 8*pi - pi/6 = -2*pi - pi/6. sin(-2*pi - pi/6) = sin(-pi/6) = -1/2. Thus, a = -2 * 36*pi^2 * (-1/2) = 36*pi^2.

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

The waves in which the particles of the medium travel in the same direction as the waves are called :

  1. linear waves

  2. longitudinal waves

  3. transverse waves

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

The waves in which the particles of the medium travel in the same direction as the waves are called longitudinal waves. 

Example:sound waves, seismic waves.

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

Wave on water surface are

  1. Longitudinal

  2. Transverse

  3. Combination of longitudinal and transverse.

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

$Answer:-$ C option

Ocean waves are both longitudinal and transverse. Technically, they're a special category called surface waves. 

At the surface of the water (or generally any place two fluids of different densities meet) the force of gravity acts as the "returning" force required for transverse waves to propagate. Gravity wants to level out the surface of the water, so peaks try to flatten and troughs try to fill. This is somewhat similar to the way a guitar string tries to return to a straight line after being plucked. 

However there is essentially zero shear strength in water, so pure transverse waves would die out extremely quickly. The trick comes from the fact that the water in an ocean wave does not move with the wave itself -- each bit of water can only give its neighbors a push, not flow. This push increases the local pressure in the water, which allows the wave to become deeper/higher.

If you could see the bulk pressure/motion of the water column below the surface, you would immediately see the fact that the "wave" is mostly a localized upswell caused by an actual submerged longitudinal pressure wave. Or you could say the upswell from the wave causes a submerged longitudinal pressure wave beneath it! Two ways to say the same thing. Dynamic fluid behavior is tricky like that. 

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

The waves produced by a motor boat sailing in water are

  1. transverse

  2. longitudinal

  3. longitudinal and transverse

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

When a motor boat sails in water , waves will be produced on the surface of the water. We know that water waves are a combination of longitudinal and transverse waves as the particles move in a circular path.