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 option a: relativity the nature of light speed of light and optical density introduction to light

The velocity of electromagnetic waves in a dielectric medium $\left( { \varepsilon  } _{ r }=2 \right) $ is:

  1. $3\times { 10 }^{ 8 }$ meter/second
  2. $1.5\times { 10 }^{ 8 }$ meter/second
  3. $6\times { 10 }^{ 8 }$ meter/second
  4. $7.5\times { 10 }^{ 7 }$ meter/second
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
It turns out that electromagnetic waves cannot propagate very far through a conducting medium before they are either absorbed or reflected. However, electromagnetic waves are able to propagate through transparent dielectric media without difficultly. The speed of electromagnetic waves propagating through a dielectric medium is given by 
$c'=\dfrac{c}{\epsilon _r}$
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The amplitudes $E _{0}$ and $B _{0}$ of electric and the magnetic component of an electromagnetic wave respectively are related to the velocity $c$ in vacuum as

  1. $E _{0}B _{0} = \dfrac {1}{c}$
  2. $E _{0} = \dfrac {c}{B _{0}}$
  3. $B _{0} = cE _{0}$
  4. $E _{0} = cB _{0}$
  5. $E _{0} = c^{3}B _{0}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As we know, in electromagnetic waves, speed or light,
$c = \dfrac {E _{0}}{B _{0}} \Rightarrow E _{0} = cB _{0}$.

Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

An electromagnetic wave passing through the space is given by equations $E=E _o\sin(wt-kx), B=B _0\sin(wt-kx)$ which of the following is true?

  1. $E _oB _0=wk$
  2. $E _ow=B _ok$
  3. $E _ok=B _ow$
  4. $E _owk=B _o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As $\dfrac{E _o}{B _o}=c$ (a)

where $c=$speed of light
$c=\nu \lambda$
Also
$w=2\pi \nu$ (1)
$k=\dfrac{2\pi}{\lambda}$ (2)
Dividing (2) by (1)
$\dfrac{w}{k}=\dfrac{2\pi \nu}{\dfrac{2\pi}{\lambda}}=\nu \lambda=c$ 
Hence (a) becomes
$\dfrac{E _o}{B _o}=\dfrac{w}{k}$
$E _ok=B _ow$
Hence the correct option is (C).



Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The wave function (in S.I. units) for an electromagnetic wave is given as-
$\psi (x, t) = 10^{3} \sin \pi (3\times 10^{6} x - 9\times 10^{14}t)$ The speed of the wave is:

  1. $9\times 10^{14} m/s$
  2. $3\times 10^{8} m/s$
  3. $3\times 10^{6} m/s$
  4. $3\times 10^{7} m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given: The wave function (in S.I. units) for an electromagnetic wave is given as- $\psi(x, t)=10^3\sin\pi(3\times 10^6x-9\times10^{14}t)$
To find the speed of the wave
Solution: 
We know electromagnetic wave eqution is
$E=E _0\cos(kz-\omega t)$
And given equation is
$\psi(x, t)=10^3\sin\pi(3\times 10^6x-9\times10^{14}t)$
By comparing these two, we get
$\omega=9\times10^{14}$ and 
$k=3\times10^6$
we also know,
Speed of electromagnetic wave, $v=\dfrac \omega k$
where v is the speed of the light
Hence, $v=\dfrac {9\times10^{14}}{3\times10^6}\\\implies v=3\times10^{8}m/s$
is the speed of the wave
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The electric field part of an electromagnetic wave in a medium is represented by $ { E } _{ x }=0 $ ;
$ { E } _{ y }=2.5\frac { N }{ C } cos[(2\pi \times { 10 }^{ 6 }\frac { rad }{ s } )t-(\pi \times { 10 }^{ -2 }\frac { rad }{ m } )x] $ ;
$ { E } _{ z }=0 $.The wave is:

  1. Moving along -x direction with frequency $ { 10 }^{ 6 } $ Hz and wave length 200 m.
  2. Moving along y direction with frequency $ 2\pi \times 10^{ 6 } $ Hz and wave length 200 m.

  3. A and B both .

  4. None of them .
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics option a: relativity the nature of light speed of light and optical density introduction to light

The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon} _{0}$ and permeability ${\mu} _{0}$ is given by :

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

Velocity of electromagnetic radiation is the velocity of light $\left(c\right)$, i.e.,
$c=\dfrac { 1 }{ \sqrt { { \mu  } _{ 0 }{ \varepsilon  } _{ 0 } }  } $
where ${ \mu  } _{ 0 }$ is the permeability and ${ \varepsilon  } _{ 0 }$ is the permittivity of free space.

Multiple choice physics free, damped and forced oscillations resonance: examples and uses resonance oscillatory motion

Pick the wrong statement:

Interference to occur:

  1. frequency of one wave should be equal to another

  2. amplitude of one wave should be comparable to that of another

  3. one wave must superpose on another

  4. frequency of two waves can never be same / equal
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interference is a phenomenon in which two waves of equal frequencies and nearly equal amplitudes superpose on one another and produce a resultant new wave.

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction . At a particular point in space and time, $\overrightarrow { E } $ = 6.3 $\hat j$ V ${m}^{-1}$. At this point $\overrightarrow { B } $ is equal to

  1. $8.33\ \times { 10 }^{ -8 }\hat { k }\ T$
  2. $18.9\ \times { 10 }^{ -8 }\hat { k }\ T$
  3. $4.1\ \times { 10 }^{ -8 }\hat { k }\ T$
  4. $2.1\ \times { 10 }^{ -8 }\hat { k }\ T$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given: The Electric field intensity due to electromagnetic waves is, $E _0=6.3\ V/m$

To find: The direction and intensity of the magnetic field of Electromagnetic wave.

The magnetic field intensity due to the wave is given by
$B _0=\dfrac{E _0}{C}$

$\Rightarrow B _0=\dfrac{6.3}{3\times 10^8}=2.1\times 10^{-8}$ Tesla

Since the propagation of the wave is along $\hat i$ (X-direction) and the electric field vector is along $\hat j$, the magnetic field of the wave should lie perpendicular to both the direction of propagation and direction of electric field.

So, $\vec B$ should be along $\vec k$ such that $\vec E\times \vec B$ should give $\hat i$ ( propagation in X-direction).

$\Rightarrow \vec B=B _0\hat k$
$\vec B=2.1\times 10^{-8}\ T\ \hat k$

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

Which one of the following is a property of a monochromatic, plane electromagnetic wave in free space?

  1. Electric and magnetic fields have a phase difference of ${\pi}/{2}$

  2. The energy contribution of both electric and magnetic fields are equal
  3. The direction of propagation is in the direction of $\overline { B } \times \overline { E } $

  4. The pressure exerted by the wave is the product of its speed and energy density.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The energy contribution of both electric and magnetic fields are equal, Energy density is written as $E=\dfrac 12\epsilon _0E^2=\dfrac{B^2}{2 \mu _0}$

And the direction of propagation of wave is written as $\hat V= \hat E\times \hat B$
Option B

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

The waves that are propagated by simultaneous periodic variations of electric and magnetic field intensity known as:

  1. Transverse wave

  2. Longitudinal wave

  3. Electromagnetic wave

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

Maxwell predicted that an accelerated charge produces a sinusoidal time varying magnetic field, which in turn produces a sinusoidal time varying electric field. These two fields are mutually perpendicular to each other and sources of each other. They (fields) form an electromagnetic wave i.e. the wave that is propagated by simultaneous periodic variations of electric field and magnetic field intensity.

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

As speed decreases, if we change medium of electromagnetic waves from air to water, frequency

  1. also decreases.

  2. also increases.

  3. remains same.

  4. may increase or decrease.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As speed decreases, if change medium of electromagnetic wave from air to water, frequency remains same.

As we go from one medium to another the frequency stays same, but the wavelength changes. Change in speed is proportional to change in wavelength.

Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

A plane electromagnetic wave of angular frequency ${ mm }^{ 2 }$ propagates in a poorly conducting medium of conductivity $\sigma $ and relative permittivity $\epsilon $ Find the ratio of conduction current density and displacement current density in the medium.

  1. ${ \epsilon \epsilon } _{ 0 }\omega /\sigma $
  2. $\sigma /{ \epsilon \epsilon } _{ \sigma }\omega $
  3. $\omega /{ \sigma \epsilon } _{ 0 }\omega $
  4. $\omega \sigma /{ \epsilon } _{ 0 }\epsilon $
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice the nature of electromagnetic waves space exploration and forms of light observing space: telescopes electromagnetic waves physics

An electromagnetic wave with frequency $\omega$ and wavelength $\lambda$ travels in the $+y$ direction. Its magnetic field is along $-x$ axis. The vector equation for the associated electric field (of amplitude E_0)is :

  1. $ \vec { E } = E _0 \cos \left(\omega t -\dfrac{2\pi}{\lambda}y\right)\hat{x}$
  2. $\vec{ E } = -E _0 \cos \left(\omega t +\dfrac{2\pi}{\lambda}y\right)\hat{x}$
  3. $-\vec{ E } = E _0 \cos \left(\omega t +\dfrac{2\pi}{\lambda}y\right)\hat{z}$
  4. $\vec { E } = E _0 \cos \left(\omega t -\dfrac{2\pi}{\lambda}y\right)\hat{z}$
Reveal answer Fill a bubble to check yourself
A Correct answer