Tag: problems on properties of waves

Questions Related to problems on properties of waves

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

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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

Show answer
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

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Correct Option: D

Phase difference between a compression and its successful rarefaction is $2 \pi $radians

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

  1. True

  2. False

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Correct Option: B
Explanation:

Phase difference between a crest and its successive trough is $ \pi $radians

A travelling wave has a velocity of 400 m/s and has a wavelength of 0.5 m. What is the phase difference between two points in the wave that are 1.25 milli secs apart

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

  1. $2 \pi$

  2. $2 \pi/3$

  3. $2 \pi/5$

  4. $ \pi/6$

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Correct Option: A
Explanation:

The frequency of the wave is $f = v/\lambda=400/0.5=800 Hz$

Time period = 1/800 = 1.25 ms

Thus, both the points are one time period apart. Hence their phase difference will be zero or $2 \pi$

The correct option is (a)

Two waves of frequencies 20 Hz and 30 Hz travels out from a common point. The phase difference between them after 0.6 sec is

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

  1. $12\pi $

  2. ${\pi \over 2}$

  3. $\pi $

  4. ${{3\pi } \over 4}$

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Correct Option: A
Explanation:

Beats period$=\cfrac{1}{30-20}=0.1second\ \Delta Y=\cfrac{2\pi}{T}\Delta t\ \quad=\cfrac{2\pi}{0.1}\times0.6=2\pi\times6=12\pi\ \therefore\Delta Y=12\pi$