Phase Difference

Q. The equation of a stationary and a travelling waves are $y_1=a\sin kx\cos \omega t$ and $y_2=a\sin (\omega t-kx)$ respectively. The phase difference between two points, $x_1=\frac{\pi }{3k}$ and $x_2=\frac{3\pi }{2k}$ is ${\varphi }_1$ in the standing wave $y_1$ and is ${\varphi }_2$ in travelling wave $y_2$ then the ratio $\frac{{\varphi }_1}{{\varphi }_2}$ is

1. $\frac{5}{6}$
2. $\frac{3}{4}$
3. $\frac{6}{7}$
4. $\frac{1}{3}$

Q. The maximum intensity of fringes in Young's experiment is $I$. If one of the slits is closed, the intensity at the same point becomes $I_0$. Then relation between $I$ & $I_0$.

1. $I=I_0$
2. $I=2I_0$
3. $I=4I_0$
4. These is no relation

Q. Two simple harmonic motions are represented by the equations $y_1=0.1sin(100\pi t+\frac{\pi }{3})$ and $y_2=0.1cos\pi t$The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 at t= 0 is

1. 
2. 
3. 
4. 

Q.

For the travelling harmonic wave y (x, t) = 2.0 cos $2\pi (10t-0.0080x+0.35)$ where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of

(a) 4 m
(b) 0.5 m
(c) $\frac{\lambda }{2}$
(d) $\frac{3\lambda }{4}$

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 $\text{cm}$ and time in $\text{s}$. 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. The differential equation of $SHM$ for a particle is given by $a\frac{d^{2}x}{d{t}^2}+bx=0$. The ratio of the maximum acceleration to the maximum velocity of the particle is

1. $\sqrt{\frac{b}{a}}$
   
2. $\frac{a}{b}$
   
3. $\frac{b}{a}$
   
4. $\sqrt{\frac{a}{b}}$
   

Q.

Derivation and condition for coherent and incoherent waves addition.

Q. What is reduced mass?

Q. Two waves have equations $x_1=a\sin (\omega t+{\varphi }_1)$ and $x_2=a\sin (\omega t+{\varphi }_2)$. 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. $\frac{\pi }{3}$

Q.

In Youngs double-slit experiment two slits are separated by $2mm$ and the screen is placed one meter away. When the light of wavelength $500nm$ is used, the fringe separation will be:

1. $0.75mm$

2. $0.50mm$

3. $1mm$

4. $0.25mm$

Q. In a young's double slit experiment, the slits are separated by $0.3\text{mm}$ and the screen is $1.5\text{m}$ away from the plane of slits. Distance between fourth bright fringe on both sides of central bright fringe is $2.4\text{cm}$. The frequency of light used is
$\times {10}^{14}\text{Hz}$

Q. The phase difference between two points separated by $0.8\text{m}$ in a wave of frequency $120\text{Hz}$ is $0.5\pi$. The velocity of wave will be

1. $720\text{m/s}$
2. $384\text{m/s}$
3. $256\text{m/s}$
4. $144\text{m/s}$

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.

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. Two simple harmonic motions are represented by the equations $x_1=5\sin (2\pi t+\frac{\pi }{4})$ and $x_2=5\sqrt{2}(\sin 2\pi t+\cos 2\pi t)$. The amplitude of second motion is _____ times the amplitude of first motion

Q. Two simple harmonic motions are represented by equations, $y_1=4\sin (10t+\varphi )$ and $y_2=5\cos 10t.$ What is the phase difference between their velocities?

1. $\varphi$
2. $-\varphi$
3. $\varphi +\frac{\pi }{2}$
4. $\varphi -\frac{\pi }{2}$

Q.

In Young’s double-slit arrangement, slits are separated by a gap of$0.5mm$, and the screen is placed at a distance of $0.5m$ from them. The distance between the first and the third bright fringe formed when the slits are illuminated by monochromatic light of $5890\AA$ is:

1. $1178\times {10}^{-6}m$

2. $1178\times {10}^{-9}m$

3. $5890\times {10}^{-7}m$

4. $1178\times {10}^{-12}m$

Q.

What happens when a transverse wave is reflected?

Q.

What is fringe in wave optics?

Q.

Two travelling waves produce a standing wave represented by equation $y=1.0mm\cos \left(1.57c{m}^{-1}\right)x\sin \left(78.5s^{-1}\right)t$, the node closest to the origin in the region $x>0$ will be at $x=\_\_\_\_\_\_\_\_cm$.

Q. two strings of same material are stretched to the same tension if their radii are in ratio 1:2 the respective wave velocity in them will be in ratio of

Q.

What is the ratio of velocities of light rays of wavelengths $4000°\mathrm{A}$ and $8000°\mathrm{A}$ in vacuum?

1. $1:2$

2. $1:1$

3. $2:1$

4. cannot be determined

Q. Acceptance angle $\left(\theta \right)$ for an optical fiber is defined as the maximum angle of incidence at the interface of medium (air usually) and core $(\mu =n_1)$ for which light ray enters and travel along the optical fiber. Sine of acceptance angle is known as numerical aperture of the optical fiber. Then in the given setup, what is the value of numerical aperture?

1. $\sqrt{n_1^2-n_2^2}$
2. $\frac{n_2}{n_1}$
3. $\frac{n_1}{n_2}$
4. $n_1$

Q. The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$. Choose the correct statement(s).

​

1. The speed of the wave is $4n\times ab$
2. The medium at a will be in the same phase as d after $\frac{4}{3n}\text{s}$
3. The phase difference between b and e is $\frac{3\pi }{2}$
4. The speed of the wave is $2n\times ab$

Q.

In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is $5m$ and the phase of P is ahead of that of Q by $90°$. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

1. $4:1:0$

2. $2:1:0$

3. $0:1:2$

4. $0:1:4$

Q.

A particle moves such that its acceleration a is given by a=-bx, where x is the displacement from equilibrium position and b is a constant. The period of oscillation 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. (a) Consider two coherent sources $S_1$ and $S_2$ producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by $S_1$ be given by $Y_1=acos\omega t$ and the displacement by $S_2$ be $Y_2=acos(\omega t+\varphi )$. Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be $I=4a^{2}co{s}^2\frac{\varphi }{2}$. Hence, establish the conditions for constructive and destructive interference.
(b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slits is increased; (ii) the monochromatic source is replaced by a source of white light.

Q.

Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by 1%, 3 beats are produced in 2sec, the initial frequency of vibration of each wire is:

1. 400 Hz

2. 300 Hz

3. 500 Hz

4. 1000 Hz

Q. Two sources are called coherent if they produce waves,

$\left(i\right)$ of equal frequency

$\left(ii\right)$ having same shape of wave front

$\left(iii\right)$ having constant phase difference

$\left(iv\right)$ of equal velocity

1. $\left(i\right)$, $\left(ii\right)$ and $\left(iv\right)$
2. $\left(i\right)$, and $\left(iii\right)$
3. $\left(ii\right)$ and $\left(iii\right)$
4. $\left(i\right)$, $\left(ii\right)$, $\left(iii\right)$ and $\left(iv\right)$