Phase Difference

Q.

If a simple harmonic oscillator has got a displacement of 0.02 m and acceleration equal to 2.0$m{s}^{-1}$ at any time, the angular frequency of the oscillator is equal to

1. 10rads^-1

2. 0.1rads^-1

3. 100rads^-1

4. rads^-1

Q.

There is a destructive interference between the two waves of wavelength l coming from two different paths at a point. To get maximum sound or constructive interference at that point, the path of one wave is to be increased by

[MP PET 1985]

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. $0$

2. $\frac{11\pi }{2}$

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

4. $\frac{3\pi }{8}$

Q.

Coherent sources are characterized by the same

[KCET 1993]

1. Phase and phase velocity

2. Wavelength, amplitude and phase velocity

3. Wavelength, amplitude and frequency

4. Wavelength and phase

Q.

If two waves of same frequency and same amplitude respectively, on superimposition produced a resultant disturbance of the same amplitude, the waves differ in phase by

[MP PMT 1990; MP PET 2000]

1. 

2. 

3. Zero

4. 

Q. Equation of a progressive wave is given by $y=0.2\text{cos}\pi (0.04t+0.02x-\frac{\pi }{6})$
where distances are in $\text{centimeter}$ and time in $\text{seconds}$. What will be the minimum distance between two particles having phase difference of $\frac{\pi }{2}$?

1. $4\text{cm}$
2. $8\text{cm}$
3. $25\text{cm}$
4. $10\text{cm}$

Q. Coherent sources are characterized by

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

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.

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. Two sources are producing waves on the same string, they interfere constructively at a point A. The disturbances produced by the two sources have to be:

1. Maximum disturbance
2. Minimum disturbance
3. Any disturbances
4. The same disturbances (same phase)

Q. A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :
(a) $y=asin{2\pi }^{t/T}$
(b) y = a sin $\upsilon$ t
(c) y = (a/T) sin t/a
(d) y = (a/$\sqrt{2}$) (sin 2$\pi$ / T + cos 2$\pi$ / T)
(a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.

Q. In Young's double slit experiment, the wavelength of light used is doubled and the distance between the two slits is halved, the new fringe width becomes,

1. $3\text{times}$
2. $\frac{1}{2}\text{times}$
3. $4\text{times}$
4. $2\text{times}$

Q. Condition of superimposition of 1) standing wave 2)progress wave

Q. A ray of light is travelling through air. Find the thickness of a glass plate which will produce a change in optical path equal to one fourth of the wavelength $\left(\lambda \right)$ of light, passing normally through it. The refractive index of glass is $\mu$.

1. $\frac{4(\mu -1)}{\lambda }$
2. $\frac{\lambda }{4(\mu -1)}$
3. $\frac{\lambda }{4\mu }$
4. $\frac{4\mu }{\lambda }$

Q. A U tube of uniform cross sectional area contains mercury upto height h in either limb. The mercury in one limb is depressed a little and then released. Obtain an expression for the time period of oscillation.

Q. A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the phase difference between two displacements of a certain point on the wave, whose time difference is $0.002\text{s}$.

1. $\pi$
2. $2.7\pi$
3. $1000\pi$
4. $\frac{\pi }{2}$

Q. Two waves have equations $x_1=a\sin (kx-\omega t+{\varphi }_1)$ and $x_2=a\sin (kx-\omega t+{\varphi }_2)$. If in the resultant wave the frequency and amplitude remain equal to amplitude and frequency of each superimposing waves, the phase difference between them is

1. $\frac{\pi }{6}$
2. $\frac{2\pi }{3}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{3}$