Tag: waves

Questions Related to waves

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. $15 \mathrm { m } / \mathrm { s }$


Correct Option: C
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 $10\,m{{s}^{-1}}$

 

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. $0 ^ { \circ }$


Correct Option: A
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


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. $\dfrac { 1 }{ 360 } s$


Correct Option: D

The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 0.5 $\pi $ the wave velocity is

  1. 144 ${ ms }^{ -1 }$

  2. 384 ${ ms }^{ -1 }$

  3. 256 ${ ms }^{ -1 }$

  4. 720 ${ ms }^{ -1 }$


Correct Option: A

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


Correct Option: B

Two waves have equations ${x} _{1}=a\sin{(\omega t+{\phi} _{1})}$ and ${x} _{2}=a\sin{(\omega t+{\phi} _{2})}$. If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves. The phase difference between them is:

  1. ${\pi}/{6}$

  2. ${2\pi}/{3}$

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

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


Correct Option: A

Two particles executing SHM of same frequency, meet at x=+A/2, while moving in opposite directions. Phase difference between the particles is 

  1. $\frac{\pi}{6}$

  2. $\frac{\pi}{3}$

  3. $\frac{5\pi}{6}$

  4. $\frac{2\pi}{3}$


Correct Option: D

Consider the wave represented by $y=\cos(500t-70x)$ where $x$ is in metres and $t$ in seconds. the two nearest points in the same phase have a separation of 

  1. $2\pi/7\ m$

  2. $2\pi/7\ cm$

  3. $20\pi/7\ m$

  4. $20\pi/7\ cm$


Correct Option: D

Four waves are expressed as
(i) $y _ { 1 } = a _ { 1 } \sin \omega t$                                            (ii) $y _ { 2 } = a _ { 2 } \sin 2 \omega t$
(iii) $y _ { 3 } = a _ { 3 } \cos \omega t$                                         (iv) $y _ { 4 } = a _ { 4 } \sin ( \omega t + \phi )$
The interference is possible between

  1. (i) and (iii)

  2. (i) and (ii)

  3. (ii) and (iv)

  4. Not possible at all


Correct Option: B
Explanation:
For interference frequency should be same.
Ans. (A)

If x=$\theta sin(\alpha + \dfrac{\pi}{6})$ and $x^1 = {\theta}cos\alpha$,then what is the phase difference between the two waves.

  1. $\pi/3$

  2. $\pi/6$

  3. $\pi/2$

  4. $\pi$


Correct Option: C