Questions Related to physics

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.

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

The distance between two consecutive crests in a wave train produced in string is 5 m. If two complete waves pass through any point per second, the velocity of wave is:

  1. $2.5 \mathrm { m } / \mathrm { s }$
  2. $5 \mathrm { m } / \mathrm { s }$
  3. $10 \mathrm { m } / \mathrm { s }$
  4. $15 \mathrm { m } / \mathrm { s }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,

Two consecutive crest =$5\,m$.

Two wave cross in time, $t=\,1\sec $

Wavelength = distance between two consecutive crest

$\lambda =5\,m$

Velocity, $v=\dfrac{2\lambda }{t}=\dfrac{2\times 5}{1}=10\,m{{s}^{-1}}$

Hence, wave speed is $10\,m{{s}^{-1}}$

 

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

Two waves $E _ { 1 } = E _ { 0 } \sin \omega t$  and $E _ { 2 } = E _ { 0 } \sin ( \omega t + 60 )$ superimpose each other. Find out initial phase of resultant wave?

  1. $30 ^ { \circ }$
  2. $60 ^ { \circ }$
  3. $120 ^ { \circ }$
  4. $0 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the resultant wave be 
$E=E0' \sin (wt+\phi)$./ Then 
$E=E _1+E _2$
$E=E _0\sin wt +E _0\sin (wt+60^o)$
$E=E _0(\sin wt +\sin (wt +60^o)$
As $\sin \cos +\sin (B)=2\sin \left (\dfrac {A+B}{2}\right) \cos \left (\dfrac {B-A}{2}\right) $
$\sin wt +\sin (wt +60^o)=2 \sin (wt +30^o).\cos (wt)$
So, $E=2E _0 \cos (wt) \sin (wt+30^o)$
So, $E _0=2E _0 \cos wt $ and $ \phi =30^o$
Option $A$ is correct


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

If the frequency of ac is 60 Hz the time difference corresponding to a phase difference of ${ 60 }^{ \circ  }$ is 

  1. 60 s

  2. 1 s

  3. $\dfrac { 1 }{ 60 } s$
  4. $\dfrac { 1 }{ 360 } s$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A 60° phase difference represents 60/360 = 1/6 of a complete cycle. For a 60 Hz AC supply, the time period T = 1/f = 1/60 seconds. The time difference for 60° = (1/6) × (1/60) = 1/360 seconds. Option D matches this calculation.

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

Two waves are represented by the equations $y _{1}a sin (\omega t+kx+0.57)m$ $y _{2}a cos (\omega t+kx)m$  
where x in meter and t in Sec.  the phase difference between them is 

  1. 0.57 radian

  2. 1.0 radian

  3. 1.25 radian

  4. 1.57 radian

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

Convert y2 to sine form: y2 = a sin(omega*t + kx + pi/2). The phase of y1 is omega*t + kx + 0.57. The phase of y2 is omega*t + kx + 1.57. The difference is 1.57 - 0.57 = 1.0 radian.