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 and noise musical sound and scale pleasant, unpleasant sounds and noise pollution sound noise and pollution

Amplitude of wave is:

  1. the distance wave moves in one second

  2. distance wave moves in one time period of wave

  3. maximum distance moved by medium particles on either side of mean position

  4. distance equal to 1 wavelength
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amplitude is the maximum distance moved by medium particles on either side of mean position.

Multiple choice physics superposition of waves coherence young's double slit experiment interference

If two sources have a randomly varying phase difference $\varphi ( t )$  the resultant intensity will be given by 

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

Phase difference is $\phi (t)$,

Since, the phase difference is varying, then the waves are said to be incoherent. So, the intensity of resultant wave is the sum of intensities of each wave i.e. $2\,{{I} _{0}}$ 

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Two sources are called coherent if they produce waves

  1. of equal wavelength

  2. of equal velocity

  3. having same shape of wavefront

  4. having a constant phase different
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Two source are called coherent, if they have constant phase difference i.e., phase difference between two wave is constant with respect to time.

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Two waves having the same wavelength and amplitude but having a constant phase difference with time are known as :

  1. identical waves

  2. incoherent waves

  3. coherent waves

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

When the light waves are emitted from a single source and they have a constant phase difference between them then the waves are said to be coherent.
Option C is correct .

Multiple choice physics superposition of waves coherence young's double slit experiment interference

The equations of waves emitted $S _1,S _2,S _3$ and $S _4$ are respectively $y _1=20\sin(100\pi t), y _2=20\sin(200\pi t), y _3=20\cos(100\pi t)$ and $y _4=20\cos(100\pi t)$. The phenomenon of interference will be produced by 

  1. $y _1$ and $y _2$
  2. $y _2$ and $y _3$
  3. $y _1$ and $y _3$

  4. Interference will not possible
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
To set up a stable and clear interference pattern, two conditions must be met:
The sources of the waves must be coherent, which means they emit identical waves with a constant phase difference.
And the waves should be monochromatic - they should be of a single wavelength.
Since the frequency of $y _1$ and $y _2$ is same, they form interference pattern.
Multiple choice physics superposition of waves coherence young's double slit experiment interference

For interference to take place

  1. sources must be coherent

  2. sources must have same amplitude

  3. waves should travel in opposite directions

  4. sources must have same frequency
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

For interference to take place source must be coherent, which implies:

  • Same frequency for the two waves
  • Constant phase difference.
Options A and D match.

Multiple choice physics refraction of light optical fibre the critical angle, total internal reflection and optical fibre total internal reflection

A plane sound wave travelling with velocity $v$ in a medium $A$ reaches a point on the interface of medium $A$ and medium $B$. If velocity of sound in medium $B$ is $2v$, the angle of incidence for total internal reflection of the wave will be greater than ($\sin{30} = 0.5$ and $\sin{90} = 1$)

  1. $15$
  2. $30$
  3. $45$
  4. $90$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Light travel from medium $A$ with velocity $v$ to medium $B$ with velocity $2v$
Velocity is more in medium $B$, hence it is rarer.
Refractive index of medium $A$ with respect to medium $B$
$\mu = _{B}{\mu} _{A} = \dfrac{Velocity  \ in \  medium \  B}{Velocity \  in   \ medium  \ A}$
$ _{B}{\mu} _{A} = {2}/{1}$
Now as       $\sin{C} = \dfrac{1}{\mu} $

$   \therefore   \sin{C} = \dfrac{1}{2} = 0.5$
$\Rightarrow        C = 30$

Multiple choice intensity and loudness waves physics

The intensity level due to two waves of the same frequency in a given medium are 1 dB and 4 dB. The ratio of their amplitude is

  1. $1 : 10^4$
  2. $1 : 4$
  3. $1 : 2$
  4. $1 : 10^{0.15}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Loudness of the sound       $L = 10  log _{10} \dfrac{I}{I _o}$


$L _2 -L _1 = 10  log _{10} \dfrac{I _2}{I _1}$

As  intensity of the wave is directly proportional to the square of the 
amplitude,    i.e       $I   \propto    A^2$

$\implies  $ $L _2 -L _1 = 20  log _{10} \dfrac{A _2}{A _1}$

$4 -  1 = 20  \log _{10} \dfrac{A _2}{A _1}$

Thus   $\dfrac{A _2}{A _1} =   10^{0.15}$

Multiple choice physics observing space: telescopes maxwell's equations the nature of light introduction to electromagnetic waves

The direction of propagation of electromagnetic wave is along.

  1. Electric field vector, $\vec{E}$
  2. Magnetic field vector, $\vec{B}$
  3. $\vec{E}\cdot \vec{B}$
  4. $\vec{E}\times \vec{B}$
  5. $\vec{B}\times \vec{E}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The direction of propagation of the electromagnetic wave is always perpendicular to the plane in which $\vec{E}$  and  $\vec{B}$ lies.
So, the direction of the propagation of the wave, $\vec{C}=E\times B$.
So, the correct option is $(D)$
Multiple choice laws of vibrations of stretched strings sonometer and laws of transverse vibrations vibrations of stretched strings waves physics

A transverse wave of amplitude 0.50m, wavelength 1m and frequency 2 Hz is propagating on a string in the negative x direction  The expression form of the wave is

  1. $\displaystyle y\left ( x,t \right )=0.5\sin \left ( 2\pi x-4\pi t \right )$
  2. $\displaystyle y\left ( x,t \right )=0.5\cos \left ( 2\pi x+4\pi t \right )$
  3. $\displaystyle y\left ( x,t \right )=0.5\sin \left ( \pi x-2\pi t \right )$
  4. $\displaystyle y\left ( x,t \right )=0.5\cos \left ( 2\pi x-2\pi t \right )$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The correct answer is B


Given below of the solution query

$y(x,t)=Asin(kx+wt)=0.5cos(\dfrac{2\pi}{\lambda }x+2\pi ft)$

$\Rightarrow y(x,t)=0.5cos(\dfrac{2\pi}{1}x+2\pi\times2t)$

$\Rightarrow y(x,t)=0.5cos(2\pi x+4\pi t)$

Multiple choice laws of vibrations of stretched strings sonometer and laws of transverse vibrations vibrations of stretched strings waves physics

A transverse wave on a string is given by $\displaystyle y=A\sin \left [ \alpha x+\beta t+\frac{\pi }{6} \right ]$ If $\displaystyle \alpha =0.56/cm,\beta =12/sec,A=7.5cm $ then find the displacement and velocity of oscillation at x = 1 cm and t = 1 s is

  1. $\displaystyle 4.6cm,46.5cm\: s^{-1}$
  2. $\displaystyle 3.75cm,77.94cm\: s^{-1}$
  3. $\displaystyle 1.76cm,7.5cm\: s^{-1}$
  4. $\displaystyle 7.5cm,75cm\: s^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Displacement y = A sin(alpha*x + beta*t + pi/6). At x=1, t=1: y = 7.5 * sin(0.56 + 12 + 0.52) = 7.5 * sin(13.08). Velocity v = dy/dt = A*beta*cos(alpha*x + beta*t + pi/6). Calculating these values yields approximately 3.75cm and 77.94 cm/s.

Multiple choice laws of vibrations of stretched strings sonometer and laws of transverse vibrations vibrations of stretched strings waves physics

A transverse wave is described by the equation $\displaystyle Y=Y _{0}\sin 2\pi \left ( ft-x/\lambda  \right )$. The maximum particle velocity is equal to four times the wave velocity if

  1. $\displaystyle \lambda =\pi Y _{0}/4 $
  2. $\displaystyle \lambda =\pi Y _{0}/2 $
  3. $\displaystyle \lambda =\pi Y _{0} $
  4. $\displaystyle \lambda =2\pi Y _{0} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$y={ Y } _{ 0 }\sin { 2\pi \left( ft-\frac { x }{ \lambda  }  \right)  } $

Maximum particle velocity
${ V } _{ max }=Aw\ \Rightarrow Aw=4{ V } _{ w }(given)\ Aw=4\left( \frac { w }{ k }  \right) \ A=\frac { 4 }{ k } \ A=\frac { 4 }{ { 2\pi  }/{ \lambda  } } \ \Rightarrow \lambda =\frac { 2\pi A }{ 4 } =\frac { \pi A }{ 2 } \ \left[ \lambda =\frac { \pi { Y } _{ 0 } }{ 2 }  \right] $
Hence option (B) is correct