Tag: waves

Questions Related to waves

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

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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

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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

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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.

When a transverse plane wave traverses a medium, individual particles execute periodic motion given by the equation  $y=0.25\cos(2\pi t-\pi x)$. The phase difference for two positions of same particle which are occupied by time intervals $0.4 second$ apart is

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

  1. $144^{o}$

  2. $135^{o}$

  3. $72^{o}$

  4. $108^{o}$

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Correct Option: A
Explanation:

$\omega =\dfrac{2\pi}{T}$
$T=\dfrac{2\pi}{\omega}$
$T=1sec$
$\therefore 2\pi \ rad \ in \   1 sec$
$in \ 0.4 sec \  2\pi\times 0.9$
$=144^o$

The phase difference between the particle at one compression and another particle in third compression is

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

  1. $\pi $ radians

  2. $2\pi $ radians

  3. $3\pi $ radians

  4. $4\pi $ radians

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Correct Option: D
Explanation:

phase difference between two successive compression is $2\pi $
$\therefore $ phase difference between a particle at one compression and in third compression is $2(2\pi)= 4\pi $

Reflection of a light wave at a fixed point results in a phase difference between incident and reflected wave of

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

  1. $\dfrac {3\pi}{2}$

  2. $2\pi $

  3. $\pi$ 

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

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Correct Option: B,D
Explanation:

Reflections of light at the interface between media often produce phase differences. The phase difference between incident and reflected wave is $2\pi$ and $\pi / 2$ radians.

Phase difference between a particle at a compression and a particle at the next rarefaction is

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

  1. Zero

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

  3. $\pi$

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

Show answer
Correct Option: C
Explanation:

Phase difference between two successive compression of rarefaction is $2\pi $
As  rarefaction appears between two compression, phase difference is $\pi $.

Which of the following is wrong about infrared rays?

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

  1. Infrared rays have wavelength higher than that of microwaves

  2. Infrared rays have wavelength lower than that of visible light

  3. Wavelength of these rays is of the order of $10^{-4}$ m

  4. The sources of infrared rays are always natural

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Correct Option: C

The phase difference between two waves represented by 
${y _1} = {10^{ - 6}}\sin \left[ {100t + \frac{x}{{50}} + 0.5} \right]m$
${y _2} = {10^{ - 6}}\cos \left[ {100t + \frac{x}{{50}}} \right]m$
where x is expressed in metres and t is expressed in seconds is approximately

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

  1. 1.07 rad

  2. 2.07 rad

  3. 0.5 rad

  4. 1.5 rad

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Correct Option: A
Explanation:
$y _{1}=10^{-6} \sin \left[100 t + \dfrac{x}{50}+ 0.5\right] m$
$y _{2}=10^{-6} \cos \left[100 t + \dfrac{x}{50}\right] m$
So,$y^{1}=10^{-6} \cos\left[\dfrac{\pi}{2}-\left(100 t + \dfrac{x}{50}+0.5\right)\right]$
$y^{1}=10^{-6} \cos \left[\dfrac{-\pi}{2}+100 t+\dfrac{x}{50}+0.5\right]$
$\triangle \phi =\phi _{2}-\phi _{1}$
$\phi _{2}=0$ where as $\phi _{1}=0.5-\dfrac{\pi}{2}$
So,
$\triangle \phi=\phi _{2}-\phi _{1}=\dfrac{\pi}{2}-0.5=1.07 \ rad$
option $-A$ is correct.

































Two waves of the same amplitude and frequency arrive at a point simultaneously. what should the phase difference between the waves so that amplitude of the resultant wave is double(2A) 

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

  1. $\dfrac {\pi}{2} radian$

  2. $\dfrac {2\pi}{3} radian$

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

  4. zero

Show answer
Correct Option: D