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 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

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

The velocity of a transverse wave in a stretched wire is $100ms^{-1}$. If the length of wire is doubled and tension in the string is also doubled, the final velocity of  the transverse wave in the wire is

  1. $100 ms^{-1}$
  2. $141.4 ms^{-1}$
  3. $200 ms^{-1}$
  4. $282.8 ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$v=\sqrt{\dfrac{T}{mass\ per\ unit\ length}}=100\ m/s$
when tension is double $ T$ becomes $2T$ and mass per unit length remains same
so, $v _1 = \sqrt{\dfrac{2T}{mass\ per\ unit\ length}}$
$=\sqrt{2}\times\sqrt{\dfrac T{mass\ per\ unit\ length}}$
$=\sqrt{2}\times 100$
$= 141.4 m/s$

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

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

  1. 10 m$s^{-1}$
  2. 10$\sqrt{2}$ m $s^{-1}$
  3. 4 m $s^{-1}$
  4. 2 m $s^{-1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Here $\mu=\dfrac{5}{20}kg/m=\dfrac{1}{4}kg/m$
Tension in the middle of wire,
$T=$ weight of half the wire $=\dfrac{5}{2}\times g=\dfrac{5}{2}\times 10N=25N$
As,$v=\sqrt{\dfrac{T}{\mu}}$
$\Rightarrow v=\sqrt{\dfrac{25}{1/4}}=10m/s$
Multiple choice dielectric substances and polarization dielectrics and polarisation electrostatic potential and capacitance electrostatics physics

A plane electromagnetic wave in a non magnetic dielectric medium is given by $\bar{E} = \bar{E _0} ( 4 \times 10^{-7} \times - 50 t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

  1. 2.4

  2. 5.8

  3. 8.2

  4. 4.8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given equation of wave 

$\vec{E} = \vec{E} _0 (4 \times \vec{10} x - 50 t)$
Comparing with general equation of wave,
$\vec{E} = \vec{E} _0 (kx - wt),$
we get,
$w = 50\ rad/s.$   $k = 4 \times 10^{-7} m^{-1}$
Thus velocity of wave, 
$v = \dfrac{w}{k} = \dfrac{50}{4 \times 10^{-7}} = 1.25 \times 10^8 m/s$
so, refractive index of medium,
$\mu = \dfrac{e}{v} = \dfrac{3 \times 10^8}{1.25 \times 10^8} = 2.4$
using, 
$u^2 = km.ke$     [km and ke are magnetic and dielectric di - constants]
as medium is non diamagnetic, $km = 1$
$\Rightarrow ke = \mu^2 = (2.4)^2 \Rightarrow ke = 5.76$

Multiple choice physics sound time period, frequency and amplitude of sound amplitude, time period and frequency of a vibration nature and characteristics of sound waves

If A is the amplitude of vibration, then the time taken by a wave to cover a distance of 4A is known as

  1. Time period

  2. Half the time period

  3. 1 s

  4. 0.1 s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time required to complete one vibration is T secs

In one full vibration, the particle covers a total distance of 4A

Thus, time required to cover a total distance of 4A during one vibration is T secs or 1 Time period

The correct option is (a)

Multiple choice biology coordination generation and conduction of nerve impulse generation of nerve impulse neurons and synapses

Characteristics of graded potential is

  1. Always followed by a refractory period

  2. Amplitude is always the same

  3. Duration and strength varies

  4. All or none response
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Unlike action potentials, which are 'all-or-none', graded potentials vary in amplitude and duration depending on the strength of the stimulus.

Multiple choice physics world of sounds characteristics of sound wave time period, frequency and amplitude of sound sound waves are longitudinal waves

Fill in the blank. 

In a wave, the particles of the medium do not move forward themselves, but the _________ is carried forward.

  1. disturbance

  2. frequency

  3. amplitude

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

In a wave, the particles of the medium do not move forward themselves, but the disturbance is carried forward.
Sound is produced when something vibrates. That is, a disturbance is produced.

Multiple choice physics world of sounds characteristics of sound wave time period, frequency and amplitude of sound sound waves are longitudinal waves

In wave motion particles of the medium

  1. move from one place to another

  2. do not move from one place to another

  3. vibrate about their mean positions

  4. vibrate away from their mean position
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a wave passes through a medium, the particles of the medium vibrate according to the wave about the mean positions.

Multiple choice physics world of sounds characteristics of sound wave time period, frequency and amplitude of sound sound waves are longitudinal waves

During a wave motion 

  1. no transfer of matter occurrs through the medium

  2. energy is transferred from one part of the medium to another

  3. both a and b occurs

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

During a wave motion only energy is transferred no transfer of matter occurs through the medium. Only vibrations travels not the air.

Multiple choice physics world of sounds characteristics of sound wave time period, frequency and amplitude of sound sound waves are longitudinal waves

Which are the two properties that affect wave speed ?

  1. Inertial properties and elastic properties

  2. Mass properties and elastic properties

  3. Inertial properties and bending properties

  4. Bending properties and elastic properties
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a wave, particles are moving from one place to another and again come back to the same place due to inertial properties and due to elastic properties  the wave vibrates. 

Multiple choice physics world of sounds characteristics of sound wave time period, frequency and amplitude of sound sound waves are longitudinal waves

two waves of same frequency and of intensity ${I} _{0}$ and $9{I} _{0}$ produces interference. If at a certain point the resultant intensity is $7{I} _{0}$ then the minimum phase difference between the two sound waves will be

  1. ${90}^{0}$
  2. ${150}^{0}$
  3. ${120}^{0}$
  4. ${100}^{0}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} 7{ I _{ o } }={ I _{ o } }+a{ I _{ o } }+2\sqrt { { I _{ o } } } \sqrt { x{ I _{ o } } } \cos  \Delta \phi  \ \Rightarrow 7{ I _{ o } }=10{ I _{ o } }+6\cos  \Delta \phi  \ \Rightarrow -3{ I _{ o } }=6\cos  \Delta \phi  \ \cos  \Delta \phi ={ { -1 } }{ 2 } \ \Delta \phi =\dfrac { { 2\pi  } }{ 3 } =\dfrac { { 2\times 180 } }{ 3 } ={ 120^{ 0 } } \ Hence, \ option\, \, C\, \, is\, \, correct\, \, answer. \end{array}$