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 free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

A transverse wave is passing through a medium. The maximum speed of the vibrating particle occurs when the displacement of the particle from the mean position is

  1. zero

  2. half of the amplitude

  3. equal to the amplitude

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

The maximum speed of the vibrating particle is when particle is on mean position.
In general total energy of the system remains constant. At the mean position potential energy is minimum this implies that kinetic energy will be maximum. Hence speed will be maximum. 

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Which relationship, out of those given below, represents the velocity of sound wave? 

$v=velocity,\ n=frequency,\ \lambda=wave\ length.$

  1. $\displaystyle v=\frac { \lambda }{ n } $
  2. $\displaystyle v=n\lambda $
  3. $\displaystyle v=\frac { n }{ \lambda } $
  4. $\displaystyle v=n\lambda +1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of wave is equal to product of its wavelength and frequency

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

The speed of a longitudinal wave in a mixture of hellium and neon at 300 k was found to be 758 m/s. The composition of the mixture would then be

  1. $13:3$
  2. $4:3$
  3. $2:1$
  4. $4:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When ${M} _{1}=0.004kg/mol$) is mixed with ${n} _{2}$ moles of (${M} _{2}=0.020kg/mol$), the equivalent molar mass of mix would be:

$M'=\cfrac{{n} _{1}{M} _{1}+{n} _{2}{M} _{2}}{{n} _{1}+{n} _{2}}=\cfrac{4{n} _{1}+20{n} _{2}}{1000({n} _{1}+{n} _{2})}$
Both $He$ and $Ne$ are monoatomic so for mixture $\gamma =\cfrac{5}{3}$
so, the velocity of sound
$V=\sqrt { \cfrac { rRT }{ M' }  } \Rightarrow M'=\cfrac { \gamma RT }{ { V }^{ 2 } } \left( at\quad T=300K \right) \quad $
$\Rightarrow \cfrac { 4{ n } _{ 1 }+20{ n } _{ 2 } }{ 1000\left( { n } _{ 1 }+{ n } _{ 2 } \right)  } =\cfrac { 5\times 8.31\times 300 }{ 3\times { (758) }^{ 2 } } \simeq \cfrac { 7 }{ 1000 } \Rightarrow \cfrac { { n } _{ 1 } }{ { n } _{ 2 } } \simeq 4.33=\cfrac { 13 }{ 3 } $

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

A Sound wave with an amplitude of $ 3 \mathrm { cm }$ starts towards right from origin and gets reflected at a rigid wall after a second. If the velocity of  the wave is $ 340 \mathrm { ms } ^ { - 1 }$  and it has a wavelength of $ 2 \mathrm { m } $, the equations of incident and reflected waves respectively could be

  1. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) } \\ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$
  2. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) } \\ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$
  3. $\begin{array} { l } { y = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) } \\ { y = - 3 \times 10 ^ { - 2 } \sin \pi ( 340 t - x ) \text { towards left } } \end{array}$
  4. $\begin{array} { l } { y = 3 \times 10 ^ { 2 } \sin \pi ( 340 t - x ) } \\ { I = 3 \times 10 ^ { - 2 } \sin \pi ( 340 t + x ) \text { towards left } } \end{array}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { \omega t-kx } \right)  \ \lambda =2m=\frac { { 2\pi  } }{ k }  \ \Rightarrow k=\pi  \ v=340\, m/s \ w=vk \ =240\pi  \ Now, \ y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t-\pi x } \right) \, \, towards\, right \ and, \ y=\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t+\pi x+\pi  } \right)  \ =-\left( { 3\times { { 10 }^{ -2 } } } \right) \sin  \left( { 340\pi t+\pi x } \right) \, \, \, \, \, \, \, towards\, \, left \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Sound waves are propagating in a medium. The moduli of isothermal and adiabatic elasticity of the medium are $E _T$ and $E _S$ respectively. The velocity of sound wave is proportional to

  1. $\sqrt{E _T}$
  2. $\sqrt{E _S}$
  3. $E _T$
  4. $\displaystyle\frac{E _S}{E _T}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of sound $V _s$ is given by


${V _s}^2={[\dfrac{\delta{p}}{\delta{\rho}}]} _S=E _S$

$V _s \propto \sqrt{E _S}$

Option 'B' is correct.

Multiple choice speed of sound in gas speed of a travelling wave oscillation and waves waves physics

Ultrasonic, infrasonic and audio waves travel through a medium with speeds $V _{u}, V _{i}$ and $V _a$ respectively then,

  1. $V _{u}, V _{i}$ and $V _{a}$ are equal
  2. $V _{u} > V _{a}> V _{i}$
  3. $V _{u} < V _{a} < V _{i}$
  4. $ V _{a}< V _{u} $ and $V _{u} \approx V _{i} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Velocity of sound wave in a medium is given by
$v= \sqrt{\frac{K}{\rho}}$ where K is the bulk modulus and $\rho$ is the density.
The classification of sound waves based on wavelength($\lambda$) is independent of speed of sound in the medium( speed depends on properties of a medium).
Hence, $V _u$, $V _i$ and $V _a$ are all equal.

Multiple choice physics properties of waves longitudinal and transverse waves travelling waves types of waves

Ocean waves of time period $0.01$ second have a speed $15 m/s$. What is the adjacent crest and the trough is:

  1. $15 \times 10^{-2} m$
  2. $7.5 \times 10^{-2} m$
  3. $3.25 \times 10^{-2} m$
  4. $30 \times 10^{-2} m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distance between a crest and an adjacent trough is half the wavelength (lambda/2). Wavelength = speed * time period = 15 * 0.01 = 0.15 m. Half the wavelength is 0.075 m, which is 7.5 * 10^-2 m.

Multiple choice physics properties of waves longitudinal and transverse waves travelling waves types of waves

A transverse wave travelling on a taut string is represented by $y = 0.01 \sin 2 \pi ( 10 t - x )$ where y and x are in metre and t is in second. Then

  1. The speed of the wave is 10 m/s.
  2. Closest points on the string which differ in phase by $60^o$ are $\dfrac16\ m$ apart.
  3. Maximum particle speed is $\frac { \pi } { 5 } { m } / { s }$
  4. The phase of a certain point on the string changes by $120 ^ { \circ }$ is $\dfrac1{20} $seconds
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Multiple choice physics properties of waves longitudinal and transverse waves travelling waves types of waves

What is the phase difference between two successive crests in the wave?

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

Phase difference between any two particles in a wave determines lack of harmony in the vibrating state of two particles, ie, how far one particle leads the other or lags behind the other. 
Relation of path difference and phase difference is given by
$\Delta \phi=\frac{2\pi}{\lambda}\times \Delta x$
where $\Delta x$ is path difference. 
But path difference between two crests
$\Delta x=\lambda$
Hence, $\Delta  \phi = \frac{2\pi}{\lambda}\times \lambda =2\pi$ 

Multiple choice physics properties of waves longitudinal and transverse waves travelling waves types of waves

The wave 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

The waves produced by a motorboat sailing in water are of both transverse and longitudinal type. Transverse waves are produced on the surface and longitudinal waves are produced deep inside the water.