Phase Difference

Q.

The path difference between the two waves $y_1=a_{1}sin(\omega t-\frac{2\pi x}{\lambda })and{y}_2=a_{2}cos(\omega t-\frac{2\pi x}{\lambda }+\varphi )$ is

1. 

2. 

3. 

4. 

Q. The two waves are represented by
$y_1={10}^{-6}sin(100t+\frac{x}{50}+0.5)m{y}_2={10}^{-2}cos(100t+\frac{x}{50})m$
where x is in metres and t in seconds. The phase difference between the waves is approximately:

1. 1.07 rad
2. 2.07 rad
3. 0.5 rad
4. 1.5 rad

Q.

If $x=asin[\omega t+\frac{\pi }{6}]and{x}^{\prime }=acos\omega t$, then what is the phase difference between the two waves?

1. 

2. 

3. 

4. 

Q.

Small amplitude progressive wave in a stretched string has a speed of 100 cm/s, and frequency 100 Hz. The phase difference between two points 2.75 cm apart on the string in radians, is

1. 

2. 

3. 

4. 

Q.

A simple harmonic progressive wave is represented by the equation $y=8sin2\pi (0.1x-2t)$ where x and y are in centimeters and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm along the x-direction is

1. 

2. 

3. 

4. 

Q.

Two particles of medium disturbed by the wave propagation are at $x_1=0and{x}_2=1cm$. The respective displacements (in cm) of the particles can be given by the equations: $y_1=2sin3\pi t,y_2=2sin(3\pi t-\frac{\pi }{8})$. The wave velocity is

1. 16 cm/s

2. 24 cm/s

3. 12 cm/s

4. 8 cm/s

Q.

In a medium in which a transverse progressive wave is travelling, the phase difference between two points with a separation of 1.25 cm is $\left(\frac{\pi }{4}\right)$. If the frequency of wave is 1000 Hz its velocity will be

1. 104 m/s

2. 125 m/s

3. 100 m/s

4. 10 m/s

Q. The figure shows three progressive waves A, B and C. What can be concluded from the figure that with respect to wave A?

1. The wave C is ahead by a phase angle of π/2 and the wave B lags behind by a phase angle .
2. The wave C is lag behind by a phase angle of and the wave B is ahead by a phase angle
3. The wave C is ahead by a phase angle of π and the wave B lags behind by a phase angle .
4. The wave C lags behind by a phase angle of π and the wave B is ahead by a phase angle .

Q. The phase difference between two waves represented by
$y_1={10}^{-6}\sin [100t+(x/50)+0.5]\text{m}$
$y_2={10}^{-6}\cos [100t+(x/50\left)\right]\text{m}$
Where $x$ is expressed in metre and $t$ is expressed in second, is approximately
[Take $\pi =3.14$]

1. $2.07$ radian
2. $0.5$ radian
3. $1.5$ radian
4. $1.07$ radian

Q. Coherent sources are characterized by

1. Equal phase and phase velocity of produced wave
2. Equal amplitude of produced wave
3. None of these
4. Zero or constant phase difference along with equal frequency and amplitude of produced wave