Tag: waves

Quizzes (32) Questions (233)

Questions Related to waves

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

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

  1. $2 \pi$
  2. $2 \pi/3$
  3. $2 \pi/5$
  4. $ \pi/6$
Reveal answer Fill a bubble to check yourself
A Correct answer
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)

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

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

  1. $12\pi $
  2. ${\pi \over 2}$
  3. $\pi $
  4. ${{3\pi } \over 4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

A progressive wave of wavelength 5 cm moves along +X axis. What is the phase difference between two points on the wave separated by a distance of 3 cm at any instant

  1. $3 \pi/5$
  2. $6 \pi/5$
  3. $2 \pi/5$
  4. $7 \pi/5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Phase difference = $(2\pi/5)$ path difference $\implies$ phase difference = $6 \pi/5$

The correct option is (b) 

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+\left( x/50 \right) +0.5 \right]\ m } $ and ${ y } _{ 2 }={ 10 }^{ -6 }\cos { \left[ 100t+\left( x/50 \right)  \right]\ m } $. Where $x$ is expressed in metre and $t$ is expressed in seconds, is approximately

  1. $1.07\ radian$
  2. $2.07\ radian$
  3. $0.5\ radian$
  4. $1.5\ radian$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

In a string the speed of wave is $10m/s$ and its frequency is $100$ Hz. The value of the phase difference at a distance $2.5$cm will be :

  1. $\pi/2$
  2. $\pi/8$
  3. $3\pi/2$
  4. $4\pi$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,


$f=100Hz$


$x=2.5cm$

$v=10m/s$  path difference

wavelength, $\lambda =\dfrac{v}{f}=\dfrac{10}{100}=0.1m$

The phase difference, $\phi=\dfrac{2\pi}{\lambda}\times x$

$\phi=\dfrac{2\pi}{0.1}\times 2.5\times 10^{-2}$

$\phi=\dfrac{\pi}{2}$

The correct option is A.

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

A transverse progressive wave on a stretched string has a velocity of $10ms^{-1}$ and frequency of $100Hz$. The phase difference between two particles of the string which nbare $2.5cm$ apart will be :

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

Given,


$v=10m/s$ velocity


$f=100Hz$ frequency

$\Delta=2.5cm$ path difference

wavelength, $\lambda=\dfrac{v}{f}$

$\lambda=\dfrac{10}{100}=0.1m$

Phase difference,

$\phi=\dfrac{2\pi}{\lambda}\times \Delta$

$\phi=\dfrac{2\pi}{0.1}\times 2.5\times 10^{-2}$

$\phi=\dfrac{\pi}{2}$

The correct option is D.

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

Two $SHMs$ are given by $Y _{1}= a\left[ \sin { \left( \dfrac { \pi  }{ 2 }  \right)  } t+\varphi  \right]$ and $Y _{2}= b\sin { \left[ \left( \dfrac { 2\pi t }{ 3 }  \right) +\varphi  \right]  }$ . The phase difference between these two after $'1'\ sec$ is:

  1. $\pi$
  2. $\dfrac {\pi}{2}$
  3. $\dfrac {\pi}{4}$
  4. $\dfrac {\pi}{6}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At t=1, the phase of Y1 is pi/2 + phi. The phase of Y2 is 2pi/3 + phi. The difference is 2pi/3 - pi/2 = 4pi/6 - 3pi/6 = pi/6.

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

Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega$ along the $x-axis.$ Their mean position is separated by distance $X _0(X _0 > A)$. If the maximum separation between them is $(X _0 + A ),$ the phase difference between their motion is :-

  1. $\dfrac{\pi}{4}$
  2. $\dfrac{\pi}{6}$
  3. $\dfrac{\pi}{2}$
  4. $\dfrac{\pi}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

${X _1} = A\sin \left( {wt + {\phi _1}} \right)$

${X _2} = A\sin \left( {wt + {\phi _2}} \right)$
${X _1} - {X _2} = A\left[ {2\sin \left[ {wt + \frac{{{\phi _1}}}{{{\phi _2}}}} \right]\sin \left[ {\frac{{{\phi _1} - {\phi _2}}}{2}} \right]} \right]$
$A = 2A\sin \left( {\frac{{{\phi _1} - {\phi _2}}}{2}} \right)$
$\frac{{{\phi _1} - {\phi _2}}}{2} = \frac{\pi }{6}$
${\phi _1} = \frac{\pi }{3}$
Hence,
option $(D)$ is correct answer.