Tag: oscillation and waves

Questions Related to oscillation and waves

The maximum particle velocity is $8$ times the wave velocity of a progressive wave. If the amplitude of the particle is $"a"$. The phase difference between the two particles seperated by a distance of $""x"$ is 

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. $\frac{x}{a}$

  2. $\frac{{8x}}{a}$

  3. $\frac{{3a}}{x}$

  4. $\frac{{3\pi x}}{a}$

Show answer
Correct Option: B

The particle of a medium vibrates about their mean position whenever a wave travels through that medium. The phase difference between the vibrations of two such particles

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. varies with time only

  2. varies with distance separating them only

  3. varies with time as well as distance

  4. is always zero

Show answer
Correct Option: B
Explanation:

The phase difference between the vibrations of two particles of the medium is given by :

            $\Delta \phi=\dfrac{2\pi}{\lambda}\Delta x$ 
it is clear that phase difference varies as the path difference between the particles varies, which is the distance, separating the particles.

The phase difference between two points separated 0.8 m in a wave of frequency 120 HZ is 0.5 $\pi $ the value velocity is

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. 144 ${ ms }^{ -1 }$

  2. 384 ${ ms }^{ -1 }$

  3. 256 ${ ms }^{ -1 }$

  4. 720 ${ ms }^{ -1 }$

Show answer
Correct Option: B

Two Waves of amplitudes ${ A } _{ 0 }$ and $x{ A } _{ 0 } $ pass through a region. If x >1, the difference in the maximum and minimum resultant amplitude possible is

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. $(x+1){ A } _{ 0 }$

  2. $(x-1){ A } _{ 0 }$

  3. $2x{ A } _{ 0 }$

  4. $2{ A } _{ 0 }$

Show answer
Correct Option: D

The equation of a wave is given by $Y\, =\, 5\, sin\, 10 \pi\, (t\, -\, 0.01x)$ along the x-axis. (All the quantities are expressed in SI units}. The phase difference the points separated by a distance of 10 m along x-axis is

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. $\displaystyle \frac{\pi}{2}$

  2. $\pi$

  3. $2 \pi$

  4. $\displaystyle \frac{\pi}{4}$

Show answer
Correct Option: B
Explanation:

For the given wave, $k=0.1\pi=\dfrac{2\pi}{\lambda}$
$\implies \lambda=20m$

Thus phase difference between two points separated by 10m is $\dfrac{2\pi}{\lambda}(x _2-x _1)$
$=\dfrac{2\pi}{\lambda}\times 10m=\pi$
Hence correct answer is option B.

A uniform rope of length $L$ and mass ${m _1}$ hangs vertically from a rigid support . A block of mass ${m _2}$ is attached to the free end of the rope. A transverse pulse of wavelength ${\lambda _1}$ is produced at  the lower end of the rope . the wavelength of the pulse when it reaches the top of the rope is ${\lambda _2}$. The ratio $\frac{{{\lambda _1}}}{{{\lambda _2}}}$ is:

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. $\sqrt {\dfrac{{{m _1}}}{{{m _2}}}} $

  2. $\sqrt {\dfrac{{{m _1} + {m _2}}}{{{m _2}}}} $

  3. $\sqrt {\dfrac{{{m _2}}}{{{m _1}}}} $

  4. $\sqrt {\dfrac{{{m _1} + {m _2}}}{{{m _1}}}} $

Show answer
Correct Option: D

When a wave travels in a medium, the particle displacement is given by y(xt)=0.03 sin $\pi $ (2t-0.01 x) where y and x are meters and t in seconds. The phase difference, at a given instant of time between two particle 25 m. apart in the medium, is 

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. $\frac{\pi }{8}$

  2. $\frac{\pi }{4}$

  3. $\frac{\pi }{2}$

  4. $\pi$

Show answer
Correct Option: A

The light waves from two independent monochromatic light sources are given by-
${y _1} = 2\sin  {\omega t }$ and ${y _2} = 2\cos  {\omega t }$,
then the following statement is correct 

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. Both the waves are coherent

  2. Both the waves are incoherent

  3. Both the waves have different time periods

  4. None of the above

Show answer
Correct Option: B
Explanation:

${y _1} = 2\sin \left( {\omega t - kx} \right)$
${y _2} = 2\cos \left( {\omega t - kx} \right) = 2\sin \left( {\omega t - kx + \frac{\pi }{2}} \right)$
So, Phase difference = $\frac{\pi}{2}$
Hence sources are incoherent.

The phase difference between two points is $\pi/3$. If the frequency of wave is 50 Hz, then what is the distance between two points? (given v = 330 m/s)

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. 2.2 m

  2. 1.1 m

  3. 0.6 m

  4. 1.7 m

Show answer
Correct Option: B
Explanation:

Phase difference $= \dfrac{2\pi}{\lambda}\times$path difference. 
The 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. 
From relation 
$\Delta \phi =\dfrac{2\pi}{\lambda}\times \delta x$


$\Rightarrow \Delta x = \dfrac{\lambda}{2\pi}\times \Delta \phi$    ...(i)

Also, $\lambda = \dfrac{v}{n}$      ...(ii)
Now, from Eqs. (i) and (ii), we get
$\Delta x=\dfrac{v}{2\pi n}\times \Delta \phi$

$\Rightarrow \Delta x=\dfrac{330}{2\pi\times 50}\times \dfrac{pi}{3}$
or $\Delta x = 1.1m$ 

When a transverse wave on a string is reflected from the free end, the phase change produced is ___________.

problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

  1. Zero rad

  2. $\dfrac { \pi }{ 2 } $ rad

  3. $\dfrac { 3\pi }{ 4 } $ rad

  4. $\pi$ rad

Show answer
Correct Option: A
Explanation:

For a transverse wave, a phase change of $\pi$ occurs when it is reflected from a denser medium.

When reflected from a free end, however, there is no change of phase.
Hence the correct answer is option A.