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 oscillations and waves standing waves in strings standing waves reflection of waves

The speed of mechanical waves depends on :-

  1. Density of medium

  2. Elasticity of medium

  3. Elasticity and density of medium

  4. Frequency of the wave.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The speed of a mechanical wave in a medium is determined by the medium's elastic properties (which provide the restoring force) and its inertial properties (density). Both factors are essential for wave propagation.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

A suspension bridge is to be built across valley where it is known that the wind can gust at $5\ s$ intervals. It is estimated that the speed of transverse waves along the span of the bridge would be $400\ m/s$. The danger of reasonant motions in the bridge at its fundamental frequency would be greater if the span had a length of :

  1. $2000\ m$
  2. $1000\ m$
  3. $400\ m$
  4. $80\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Resonance occurs when the driving frequency matches the natural frequency of the system. For a bridge span, the fundamental frequency is f = v / (2L). Given v = 400 m/s and a period of 5s (frequency f = 0.2 Hz), setting 0.2 = 400 / (2L) leads to 0.4L = 400, so L = 1000 m.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

The wave-function for a certain standing wave on a string fixed at both ends is $y\left( x,t \right) =0.5\sin { \left( 0.025\pi x \right)  } \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
C Correct answer
Explanation

For the shortest possible length, it should be allowing fundamental frequency resonance.

In fundamental frequency
$L=\dfrac { \lambda  }{ 2 } \quad \quad \quad \quad \left( \because K=\dfrac { 2\pi  }{ \lambda  }  \right) $
$=\dfrac { 2\pi /K }{ 2 } =\dfrac { \pi  }{ K } $
from $y=0.5\sin\left( 0.025\pi x \right) \cos\left( 500t \right) $
$K=0.025\pi \quad \quad \quad (on\quad comparing\quad with\quad y=A\sin\left( Kx \right) \cos\left( wt \right) )$
$\therefore \quad L=\dfrac { \pi  }{ 0.025\pi  } =\dfrac { 1000 }{ 25 } $
$\left[ L=40cm \right] $

Hence Option (C) is correct.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

If the difference between the frequencies of two waves is 10 Hz then time interval between successive maximum intensity is:

  1. $10 s$
  2. $1 s$
  3. $0.1 s$
  4. $0.01 s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The beat frequency is the difference between the frequencies of two waves. The time interval between successive maximum intensities (beats) is the reciprocal of the beat frequency: T = 1/10 = 0.1 s.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Statement-1:
Two longitudinal waves given by equations; ${ y } _{ 1 }$(x,t) = 2a $\sin { \left( \omega t-kx \right)  } $ and ${ y } _{ 2 }\left( x,t \right) $ = a $\sin { \left( 2\omega t-2kx \right)  } $  will have equal intensity.

Statement-2:
Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

  1. Statement-1 is true, statement -2 is true; statement-2 is not correct explanation of statement -1.

  2. Statement-1 is false, statement -2 is true.

  3. Statement-1 is true, statement -2 is false.

  4. Statement -1 is true, statement-2 true; statement-2 is the correct explanation of statement-1.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Intensity is proportional to the square of the amplitude and the square of the frequency (I proportional to A^2 * f^2). Wave 1 has amplitude 2a and frequency f, while Wave 2 has amplitude a and frequency 2f. Thus, intensities are proportional to (2a)^2 * f^2 = 4a^2f^2 and a^2 * (2f)^2 = 4a^2f^2, making them equal. Statement 2 is false because intensity depends on both amplitude and frequency.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Two coherent sources of different intensities send waves which interfere. If the ratio of maximum and minimum intensity in the interference pattern is $25$ then find ratio of intensity of source :

  1. $25 : 1$
  2. $5 : 1$
  3. $9 : 4$
  4. $25 : 16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\cfrac { { I } _{ max } }{ { I } _{ min } } ={ \left[ \cfrac { \sqrt { { I } _{ 1 } } +\sqrt { { I } _{ 2 } }  }{ \sqrt { { I } _{ 1 } } -\sqrt { { I } _{ 2 } }  }  \right]  }^{ 2 }$

Where and  are intensities of two waves 

given 

$\cfrac { { I } _{ max } }{ { I } _{ min } } =\cfrac { 25 }{ 1 } \\ \therefore \cfrac { \sqrt { { I } _{ 1 } } +\sqrt { { I } _{ 2 } }  }{ \sqrt { { I } _{ 1 } } -\sqrt { { I } _{ 2 } }  } =\cfrac { 5 }{ 1 } $

use componendo and dividendo

we get

$\cfrac { \sqrt { { I } _{ 1 } } +\sqrt { { I } _{ 2 } } +\sqrt { { I } _{ 1 } } -\sqrt { { I } _{ 2 } }  }{ \sqrt { { I } _{ 1 } } +\sqrt { { I } _{ 2 } } -\sqrt { { I } _{ 1 } } +\sqrt { { I } _{ 2 } }  } =\cfrac { 5+1 }{ 5-1 } \\ or,\quad \cfrac { \sqrt { { I } _{ 1 } }  }{ \sqrt { { I } _{ 2 } }  } =\cfrac { 3 }{ 2 } \\ or,\quad \cfrac { { I } _{ 1 } }{ { I } _{ 2 } } =\cfrac { 9 }{ 4 } $

 

 

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Statement -1:
Two longitudinal waves given by equation $y _{1}$(x,t) = 2a sin $(\omega - kx)$ and $y _{2}$(x,t) = a sin $(2\omega - 2kx)$ will have equal intensity.
Statement -2:
Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

  1. Statement -1 is true, statement -2 is true; statement -2 is not correct explanation of statement-1.

  2. Statement -1 is false, statement -2 is true.

  3. Statement -1 is true, statement -2 is false

  4. Statement -1 is true, statement -2 true; statement -2 is the correct explanation of statement -1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Intensity of waves of given frequency in same medium is not only proportional to square of amplitude. It depends on other factors also

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

If two waves maintain constant phase difference or same phase at any two points on a wave is known as spatial coherence.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Two wave sources are said to be coherent if the waves either have same phase or constant phase difference at any two points on a wave and the phenomenon is known as spatial coherence.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Intensity (I) is related to amplitude (A) as:

  1. $I \propto A$
  2. $I \propto {A^2}$
  3. $I \propto {A^4}$
  4. $I \propto {A^{-1}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Intensity of a wave is directly proportional to the square of amplitude of the wave.
i.e.  $I \propto A^2$
More is the amplitude of wave, more will be the intensity.
So, we write  $I = kA^2$
where $k$ is a proportionality constant.

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

The resultant intensity for two identical waves of intensity I with a phase difference of $\pi/3$ is 

  1. $R=2\sqrt{3I}$
  2. $R=\sqrt{3I}$
  3. $R=4\sqrt{3I}$
  4. $R=3\sqrt{3I}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The resultant of two waves is given by $R^2=A^2+B^2+2AB cos \theta; \theta$ is the phase difference and A and B are the amplitudes of the individual waves.

Since both the waves are identical, their amplitudes are equal

Thus, $R^2 = A^2+A^2+A^2=3A^2 \implies R=\sqrt{3}A$

Since intensity is proportional to $\sqrt{A}$, we can write the resultant amplitude $R = \sqrt{3I}$

The correct option is (b)

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

If the sum of the intensities of two component waves are 5I units and upon superposition with a phase difference of $\pi $ radians, their resultant is 2I, what are the intensities of component waves

  1. $I _1=3I, I _2=I$
  2. $I _1=3.5I, I _2=1.5I$
  3. $I _1=2I, I _2=3I$
  4. $I _1=I, I _2=4I$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If $I _1$ and $I _2$ are intensities of two waves, then $I _1+I _2=5I$ and $(I _1-I _2)=2I$. Solving, we get,$I _1=3.5I$ and $I _2=1.5I$

The correct option is (b)

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Waves from two sources superpose on each other at a particular point amplitude and frequency of both the waves are equal. The ratio of intensities when both waves reach in the same phase and they reach with the phase difference of $90^{\circ}$ will be

  1. $1 : 1$
  2. $\sqrt {2} : 1$
  3. $2 : 1$
  4. $4 : 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Relation between intensity $f$
Amplitude
$I= kA^{2} \cos^{2} \left( \dfrac{|theta}{2} \right)$
When both the waves reach in the same phase, then 
$\theta= 0^{o}$ 
$I _{1}= kA^{2} \cos^{2} \left( \dfrac{0^{o}}{2} \right)$
$I _{1} = kA^{2} [\cos 0^{o}=1]$ ------- $(1)$
When both the waves reach with phase difference $90^{o}$.
$\theta = 90^{o}$
$I _{2}= kA^{2} \cos^{2} \left( \dfrac{90^{o}}{2} \right)$
$I _{2} = kA^{2} \cos^{2} (45^{o})$
$I _{2}= kA^{2} \left( \dfrac{1}{2} \right)$ ----- $(2)$
$\dfrac{I _{1}}{I _{2}}= \dfrac{kA^{2}}{kA^{2} (1/2)} =\dfrac{2}{1}$
Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Suppose displacement produced at some point $P$ by a wave is $y _1=a cos \omega t$ and by another wave is $y _2=a cos \omega t$.Let $I _0$ represents intensity produced by each one of individual wave, then resultant intensity due to overlapping of both wave is

  1. $I _0$
  2. $2I _0$
  3. $\dfrac{I _0}{2}$
  4. $4I _0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$y _{res}$ at point $P=y _1+y _2\=a\cos \omega t+a\cos\omega t\=2\cos\omega t$

Now amplitude $=2a$
Since  intensity $\propto$(amplitude)$^2$
So, $\cfrac{I _{new}}{I _0}=\cfrac{4a^2}{a^2}\\implies I _{new}=4I _0$

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Two waves $Y _{1}=a\sin \omega t$ and $Y _{2}=a\sin (\omega t+\delta)$ are producing interference, then resultant intensity is-

  1. $a^{2}\cos^{2}\delta/2$
  2. $2a^{2}\cos^{2}\delta/2$
  3. $3a^{2}\cos^{2}\delta/2$
  4. $4a^{2}\cos^{2}\delta/2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The resultant intensity of two waves with equal amplitude 'a' and phase difference 'delta' is I = I1 + I2 + 2*sqrt(I1*I2)*cos(delta). With I1 = I2 = k*a^2, I = 2*k*a^2(1 + cos(delta)) = 4*k*a^2*cos^2(delta/2). Assuming k=1, the result is 4*a^2*cos^2(delta/2).

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Path difference between two waves from a coherent sources is 5 nm at a  point P. Wavelength of these waves is 100 $\mathring { A } $. Resultant intensity at point P if intensity of sources is $l _0$ and $4l _0$

  1. Zero
  2. $l _0$
  3. $5l _0$
  4. $3l _0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} \Delta x=5\times { 10^{ -9 } }m \ \Delta \phi =\frac { { 2\pi  } }{ \lambda  } \Delta x \ =\frac { { 2\pi \times 5\times { { 10 }^{ -9 } } } }{ { 100\times { { 10 }^{ -10 } } } }  \ =\pi  \ Now, \ I={ I _{ 0 } }+4{ I _{ 0 } }+2\sqrt { { I _{ 0 } } } \sqrt { 4{ I _{ 0 } } } \cos  \phi  \ =5{ I _{ 0 } }+4{ I _{ 0 } }\left[ { \cos  \pi  } \right]  \ ={ I _{ 0 } } \ \therefore resula\tan  t\, \, \, { { intensity } }\, ={ I _{ 0 } } \ Hence,\, option\, \, B\, \, is\, the\, correct\, answer. \end{array}$