Phase Difference

Q.

A wave $\mathrm{y}=\mathrm{a}\sin (\mathrm{\omega t}-\mathrm{kx})$ on a string meets with another wave producing a node at x = 0. The equation of the unknown wave is

1. $\mathrm{y}=\mathrm{a}\sin (\mathrm{\omega t}+\mathrm{kx})$

2. $\mathrm{y}=\mathrm{a}\cos (\mathrm{kx}-\mathrm{\omega t})$

3. $\mathrm{y}=-\mathrm{a}\cos (\mathrm{kx}-\mathrm{\omega t})$

4. $\mathrm{y}=-\mathrm{a}\sin (\mathrm{\omega t}+\mathrm{kx})$

Q.

The stationary waves are produced in a $20m$ long stretched string fixed at both ends. if the string vibrates in $10$ loops and the wave velocity in the string is $20m/s$, then the frequency of the wave is

Q.

On a string, the space between nodes is 5 cm. The transverse wave has a velocity of 2 ms -1. The frequency is then

1. $5\mathrm{Hz}$

2. $10\mathrm{Hz}$

3. $20\mathrm{Hz}$

4. $15\mathrm{Hz}$

Q. A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the distance between two points on a wave whose phase difference is ${45}^{\circ }.$

1. $0.625\text{cm}$
2. $0.625\text{m}$
3. $6.25\text{cm}$
4. $6.25\text{m}$

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

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

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

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

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. Two waves having same amplitude $\left(A\right)$, wavelength $\left(\lambda \right)$ and frequency $\left(f\right)$ are propagating in the same direction. They interfere such that the amplitude of resultant wave is zero. The path difference between two wave can be :

1. $\lambda$
2. $2\lambda$
3. $\frac{3\lambda }{2}$
4. $\frac{3\lambda }{4}$

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. ${18}^{\circ }$

2. ${36}^{\circ }$

3. ${54}^{\circ }$

4. ${72}^{\circ }$

Q. A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the distance between two points on a wave whose phase difference is ${45}^{\circ }.$

1. $0.625\text{cm}$
2. $0.625\text{m}$
3. $6.25\text{cm}$
4. $6.25\text{m}$

Q. Match the condition for the type of interference:
1. Constructive I. $(2n+1)\frac{\lambda }{2}$
2. Destructive II. $\left(2n\right)\lambda$

1. 1-I ; 2-II
2. 1-II ; 2-I
3. 1-II, I ; 2-I, II
4. Information insufficient

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

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

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. A wave of frequency $680\text{Hz}$ has a wave velocity of $340\text{m/s}$ . Find the distance between two points on a wave whose phase difference is ${45}^{\circ }.$

1. $0.625\text{cm}$
2. $0.625\text{m}$
3. $6.25\text{cm}$
4. $6.25\text{m}$

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. $\frac{\lambda }{2\pi }\varphi$
2. $\frac{\lambda }{2\pi }(\varphi +\frac{\pi }{2})$
3. $\frac{2\pi }{\lambda }(\varphi -\frac{\pi }{2})$
4. $\frac{2\pi }{\lambda }\varphi$

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. While conducting Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources $(S_1,S_2)$ emitting light of wavelength $600\text{nm}$. The student mistakenly placed the screen parallel to the $x-z$ plane $($for $z>0)$ at a distance $D=3\text{m}$, from the mid-point of $S_1,S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003\text{mm}$. The origin $O$ is at the intersection of the screen and the line joining $S_1,S_2$. Which of the following is(are) true of the intensity pattern on the screen?

1. Straight bright and dark bands parallel to the $x$-axis.
2. Semicircular bright and dark bands centered at point $O$.
3. Hyperbolic bright and dark bands with foci symmetrically placed about $O$ in the $x$-direction.
4. The region very close to the point $O$ will be dark.