Tag: waves

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Questions Related to waves

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

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 

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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)

  1. 2.2 m

  2. 1.1 m

  3. 0.6 m

  4. 1.7 m
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $\Delta x = 1.1m$ 

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

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

  1. Zero rad
  2. $\dfrac { \pi }{ 2 } $ rad
  3. $\dfrac { 3\pi }{ 4 } $ rad
  4. $\pi$ rad
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $144^{o}$
  2. $135^{o}$
  3. $72^{o}$
  4. $108^{o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  1. $\pi $ radians
  2. $2\pi $ radians
  3. $3\pi $ radians
  4. $4\pi $ radians
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $

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

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

  1. $\dfrac {3\pi}{2}$
  2. $2\pi $
  3. $\pi$
  4. $\dfrac {\pi}{2}$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
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.

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

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

  1. 1.07 rad

  2. 2.07 rad

  3. 0.5 rad

  4. 1.5 rad
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

































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

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) 

  1. $\dfrac {\pi}{2} radian$
  2. $\dfrac {2\pi}{3} radian$
  3. $\dfrac {3\pi}{4} radian$

  4. zero
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Resultant amplitude A_res = sqrt(A1^2 + A2^2 + 2 * A1 * A2 * cos(phi)). For A1 = A2 = A, A_res = 2 * A * cos(phi / 2). For A_res = 2 * A, cos(phi / 2) = 1, so phi / 2 = 0, which means phi = 0.