Tag: waves

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Questions Related to waves

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

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 ${ ms }^{ -1 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Phase difference is related to path difference by delta phi = (2pi / lambda) * delta x. Given delta phi = 0.5 pi and delta x = 0.8 m, we find lambda = 3.2 m. Wave velocity v = frequency * wavelength = 120 * 3.2 = 384 ms^-1.

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.

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

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. ${\pi}/{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The amplitude of the resultant of two waves with equal amplitudes a and phase difference phi is given by A = sqrt(2a^2 + 2a^2 cos(phi)). Setting the resultant amplitude equal to a gives 1 + cos(phi) = -1/2, leading to cos(phi) = -1/2, so phi = 2pi / 3.

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

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. $\frac{2\pi}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At x = A/2, the phase angles are pi/6 and 5pi/6. Since they move in opposite directions, one is at pi/6 (moving away from equilibrium) and the other is at 5pi/6 (moving toward equilibrium). The difference is 5pi/6 - pi/6 = 4pi/6 = 2pi/3.

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

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. $20\pi/7\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the same phase, the path difference must be a multiple of the wavelength. Here, k = 70, so 2pi/lambda = 70, lambda = 2pi/70 m = 2pi/70 * 100 cm = 20pi/7 cm.

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

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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
For interference frequency should be same.
Ans. (A)
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

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. $\pi$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rewriting x = theta * sin(alpha + pi/6) and x' = theta * cos(alpha) = theta * sin(alpha + pi/2), the phase difference between the two sine waves is the difference in their phase angles, which is (alpha + pi/2) - (alpha + pi/6) = pi/3.