Tag: problems on properties of waves

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

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

  1. varies with time only

  2. varies with distance separating them only

  3. varies with time as well as distance

  4. is always zero
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $(x+1){ A } _{ 0 }$
  2. $(x-1){ A } _{ 0 }$
  3. $2x{ A } _{ 0 }$
  4. $2{ A } _{ 0 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Maximum amplitude A_max = A1 + A2 = (x + 1) * A_0. Minimum amplitude A_min = |A1 - A2| = (x - 1) * A_0. The difference is A_max - A_min = (x + 1) * A_0 - (x - 1) * A_0 = 2 * A_0.

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

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

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

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

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:

  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}}}} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

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 

  1. $\frac{\pi }{8}$
  2. $\frac{\pi }{4}$
  3. $\frac{\pi }{2}$
  4. $\pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The phase difference delta phi is given by (2pi / lambda) * delta x, or from the wave equation k * delta x. Here k = 0.01 pi, so delta phi = 0.01 pi * 25 = 0.25 pi = pi / 4 radians.

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.