Interference Definition

Q. Ratio of maximum to minimum intensity during interference of two waves is $25:1$. The amplitude ratio of these two waves is

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

Q. Statement I- Two longitudinal waves given by equations $y_1(x,t)=2\text{a}\sin (\omega t-kx)$ and $y_2(x,t)=\text{a}\sin (2\omega t-2kx)$ will have equal intensity.
Statement II- Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

1. Statement I is true, statement II true; statement II is the correct explanation of statement I
2. Statement I is true, statement II is true; statement II is not correct explanation of statement I
3. Statement I is ture, statement II is false
4. Statement I is false, statement II is true

Q. Two wires having different mass densities are soldered together end to end, then stretched under tension $T$. The wave speed in the first wire is twice that in the second wire and the amplitude of incident wave is $a$. Assuming no energy losses in the wire, find the fraction of the incident power that is reflected.

1. $\frac{1}{5}$
2. $\frac{8}{9}$
3. $\frac{1}{9}$
4. $\frac{1}{2}$

Q. Two superimposing waves are represented by the equations $x_1=5\sin 2\pi (20t-0.1x)$ and $x_2=10\sin 2\pi (20t-0.2x)$ where $x$ and amplitude of each wave are given in meters and $t$ is in seconds. If the ratio of maximum intensity to minimum intensity is $x:1$, then $x$ is

Q. In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is ${\frac{1}{8}}^{\text{th}}$ of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

1. $0.853$
2. $0.672$
3. $0.568$
4. $0.760$

Q. Two waves of the same frequency and same amplitude are superimposed to produce a resultant disturbance wave of the same amplitude. What is the phase difference between the two original waves?

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

Q. Four light waves are represented by
$\left(i\right)y=a_1\sin \omega t$
$\left(ii\right)y=a_2\sin (\omega t+\varphi )$
$\left(iii\right)y=a_1\sin 2\omega t$
$\left(iv\right)y=a_2\sin 2(\omega t+\varphi )$

Interference fringes may be observed due to super position of

1. $\left(iii\right)$ and $\left(iv\right)$
2. $\left(i\right)$ and $\left(iii\right)$
3. $\left(ii\right)$ and $\left(iv\right)$
4. Interference is not possible in any combination of these four given waves.

Q. A wave given by equation $y=8\sin 2\pi (0.1x-2t)$ where $x$ and $y$ are in centimeters and $t$ is in seconds. At any instant , the phase difference between two particles, separated by $2.0\text{cm}$ along the $x$-direction, is,

1. ${18}^{\circ }$
2. ${36}^{\circ }$
3. ${54}^{\circ }$
4. ${72}^{\circ }$

Q. Two waves of equal frequencies moving in the same direction have their amplitudes in the ratio $7:5$. They are superimposed on each other. Find the ratio of maximum to minimum intensity of the resultant wave.

1. $16:25$
2. $25:16$
3. $36:1$
4. $1:36$

Q. In the shown figure, answer the following question.

If $p_i,p_r,p_t$ are powers of incident, reflected and transmitted waves and $I_i,I_r,I_t$ the corresponding intensities, then under what conditions $75\%$ of incident energy is transmitted?

1. $\frac{v_1}{v_2}=\frac{1}{2}$
2. $\frac{v_1}{v_2}=\frac{1}{3}$
3. $\frac{v_1}{v_2}=\frac{1}{4}$
4. $\frac{v_1}{v_2}=\frac{2}{3}$

Q. Two waves of equal frequencies, have their amplitudes in the ratio of $4:5$. They are superimposed on each other. Calculate the ratio of maximum and minimum intensity of the resultant wave.

1. $3:1$
2. $9:1$
3. $27:1$
4. $81:1$

Q. For the two parallel rays $\text{(AB and DE)}$ of same wavelength $\lambda$, $\text{BD}$ is the wavefront. The phase difference of these two rays at point $\text{D}$ is

1. $\frac{\sqrt{2}t\pi }{\lambda }+\pi$
2. $\frac{\sqrt{5}t\pi }{\lambda }+\pi$
3. $\frac{2\sqrt{3}t\pi }{\lambda }+\pi$
4. $\frac{t\pi }{\lambda }+\pi$

Q. There is a destructive interference between the two waves of wavelength $\lambda$ coming from two different paths at a point. To get the constructive interference at that point, the path of one wave is to be increased by,

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

Q. It is not possible to have interference between the waves produced by two violins as for interference of two waves the phase difference between the waves must.

1. remain constant
2. be zero
3. change

Q. For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for $\overrightarrow{E}$ and $\overrightarrow{B}$ field respectively?

1. $(2\hat{i}+3\hat{j})$ and $(\hat{i}+2\hat{j})$
2. $(3\hat{i}+4\hat{j})$ and $(4\hat{i}-3\hat{j})$
3. $(\hat{i}+2\hat{j})$ and $(2\hat{i}-\hat{j})$
4. $(-2\hat{i}-3\hat{j})$ and $(3\hat{i}-2\hat{j})$

Q. What do you mean by interference of light? Discuss necessary conditions for interference.

Q.

In YDSE ratio of Amplitude of wave is $1:3$. The ratio of $I_{max}:I_{min}$ is:

1. $1:4$

2. $4:1$

3. $1:1$

4. $1:9$

Q.

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at distances of $9m$ and $25m$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

1. $9:4$

2. $1:22$

3. $25:9$

4. $625:81$

Q. Two sources $S_1$ and $S_2$ are emitting light of wavelength $600\text{nm}$ are placed a distance $1.0\times {10}^{-2}\text{cm}$ apart. A detector can be moved on the line $S_{1}P$ which is perpendicular to $S_1{S}_2$. Locate the position of the farthest minima detected.

1. $D=0.85\text{cm}$
2. $D=1.7\text{cm}$
3. $D=2.55\text{cm}$
4. $D=3.4\text{cm}$

Q. Two superimposing waves are represented by the equations $x_1=5\sin 2\pi (20t-0.1x)$ and $x_2=10\sin 2\pi (20t-0.2x)$ where $x$ and amplitude of each wave are given in meters and $t$ is in seconds. Find the ratio of maximum intensity to minimum intensity.

1. $2:1$
2. $1:2$
3. $9:1$
4. $1:9$

Q. In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is ${\frac{1}{8}}^{th}$ of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:

1. $0.74$
2. $0.85$
3. $0.94$
4. $0.80$

Q. A source '$s$' is emitting waves, which travels through a tube of given shape. The detector '$D$ ' detects constructive interference of certain frequencies. If speed of wave is $v$ and $n$ is an integer then those frequencies are

1. $\frac{nv}{a}$
2. $\frac{na}{v}$
3. $\frac{a}{nv}$
4. $\frac{v}{na}$

Q. In the $EM$ wave the amplitude of magnetic field $H_0$ and the amplitude of electric field $E_0$ at any place are related as:

1. $H_0=E_0$
2. $H_0=\frac{E_0}{c}$
3. $H_0=E_0\sqrt{\frac{{\mu }_0}{{\in }_0}}$
4. $H_0=E_0\sqrt{\frac{{\in }_0}{{\mu }_0}}$

Q. The amplitude of oscillation of the image is

1. $A$
2. $2A$
3. image does not oscillate
4. $\frac{A}{2}$

Q. In the phenomenon of interference of two waves

1. Sources of the two waves must be coherent
2. Amplitude of the two waves must be same
3. Wavelength of two waves must be same
4. Intensities of the two waves can be different

Q. What is interference? Write the condition for path difference in case of constructive and destructive interference.

Q. Two waves represented by the following equations are travelling in the same medium
$y_1=5\sin 2\pi \left(75t-0.25X\right),$
$y_2=10\sin 2\pi \left(150t-0.50X\right)$
The intensity ratio $I_1/I_2$ of the two waves is $:-$

1. $1:2$
2. $1:4$
3. $1:8$
4. $1:16$

Q. In vacuum what will be common among X-rays, visible light, radio waves and infra-red rays ?

1. Speed
2. Frequency
3. Wavelength
4. Amplitude

Q. On a rainy day, small oil films on water show brilliant colours. This is due to

1. dispersion
2. interference
3. diffraction
4. polarization

Q. For constructive interference between two waves of equal wavelength, the phase angle $\delta$ should be such that :

1. $co{s}^2\frac{\delta }{2}=-1$
2. $co{s}^2\frac{\delta }{2}=1$
3. $co{s}^2\frac{\delta }{2}=0$
4. $co{s}^2\frac{\delta }{2}=\infty$