Question 1

The principle of superposition of waves states that the resultant displacement at a point is:

Accepted Answer

The vector sum of the displacements due to the individual waves. Because the wave equation is linear, each wave travels as though the other were absent and the displacements simply add.

Question 2

Constructive interference between two waves occurs when the path difference is:

Accepted Answer

An integral multiple of the wavelength. A path difference of n\lambda brings the waves into step, so their amplitudes add and the intensity is maximum.

Question 3

Destructive interference between two waves occurs when the path difference is:

Accepted Answer

An odd multiple of half the wavelength. A path difference of (2n-1)\dfrac{\lambda}{2} puts the waves exactly out of step, so the amplitudes subtract.

Question 4

A sustained interference pattern requires the two sources to be:

Accepted Answer

Coherent, maintaining a constant phase difference. If the phase relationship shifts randomly, the positions of maxima and minima move too fast to be observed and the pattern washes out.

Question 5

In an interference pattern, energy is:

Accepted Answer

Redistributed, with the total energy conserved. The energy missing from the dark fringes reappears in the bright ones, so interference redistributes energy rather than violating its conservation.

Question 6

Two waves of the same frequency travelling along the same line with zero phase difference produce a resultant of amplitude:

Accepted Answer

A_1 + A_2. With \cos\phi = 1, the general result \sqrt{A_1^2 + A_2^2 + 2A_1A_2\cos\phi} reduces to A_1 + A_2.

Question 7

The resultant intensity of two interfering waves of intensities I_1 and I_2 with phase difference \phi is:

Accepted Answer

I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi. Squaring the resultant amplitude gives this standard interference formula; the last term is the interference term that produces the fringes.

Question 8

The intensity of a wave is proportional to:

Accepted Answer

The square of its amplitude. Energy per unit volume in a wave varies as A^2, and intensity is the energy transported per unit area per unit time.

Question 9

The superposition principle holds for waves because the governing differential equation is:

Accepted Answer

Linear in the displacement. For a linear equation, any sum of solutions is itself a solution — which is exactly what superposition asserts.

Question 10

In an interference pattern, the ratio of maximum to minimum intensity is 9 : 1. The ratio of the amplitudes of the two waves is:

Accepted Answer

2 : 1. \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{A_1 + A_2}{A_1 - A_2}\right)^2 = 9 \Rightarrow \dfrac{A_1 + A_2}{A_1 - A_2} = 3 \Rightarrow \dfrac{A_1}{A_2} = \dfrac{2}{1}.

Question 11

Two interfering waves have amplitudes in the ratio 3 : 1. The ratio of maximum to minimum intensity is:

Accepted Answer

4 : 1. \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{3 + 1}{3 - 1}\right)^2 = \left(\dfrac{4}{2}\right)^2 = 4.

Question 12

Two coherent waves have intensities in the ratio 4 : 1. The ratio of maximum to minimum intensity in the pattern is:

Accepted Answer

9 : 1. Amplitudes go as \sqrt{I}, giving A_1 : A_2 = 2 : 1. Hence \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{3}{1}\right)^2 = 9.

Question 13

Two waves of amplitudes 3	ext{ cm} and 4	ext{ cm} superpose with a phase difference of 90^\circ. The resultant amplitude is:

Accepted Answer

5	ext{ cm}. With \cos 90^\circ = 0, A = \sqrt{3^2 + 4^2} = 5	ext{ cm}.

Question 14

Two waves of amplitudes 5	ext{ cm} and 3	ext{ cm} interfere. The ratio of maximum to minimum intensity is:

Accepted Answer

16 : 1. Maximum amplitude = 8	ext{ cm} and minimum = 2	ext{ cm}, so the intensity ratio is \left(\dfrac{8}{2}ight)^2 = 16.

Question 15

Two waves of equal amplitude a superpose with a phase difference of \dfrac{2\pi}{3}. The resultant amplitude is:

Accepted Answer

a. A = \sqrt{a^2 + a^2 + 2a^2\cos 120^\circ} = \sqrt{2a^2 - a^2} = a.

Question 16

Two coherent waves each of intensity I_0 interfere with zero phase difference. The resultant intensity is:

Accepted Answer

4I_0. I = 4I_0\cos^2\dfrac{\phi}{2}. With \phi = 0, I = 4I_0 — four times, not twice, the single-source intensity.

Question 17

Two coherent waves each of intensity I_0 interfere with a phase difference of \dfrac{\pi}{3}. The resultant intensity is:

Accepted Answer

3I_0. I = 4I_0\cos^2\dfrac{\phi}{2} = 4I_0\cos^2 30^\circ = 4I_0 	imes 0.75 = 3I_0.

Question 18

Two waves reaching a point have a path difference of 1.5\lambda. The interference there is:

Accepted Answer

Destructive, since the path difference is an odd multiple of \dfrac{\lambda}{2}. 1.5\lambda = 3 	imes \dfrac{\lambda}{2}, an odd multiple of half a wavelength, so the waves arrive exactly out of step.

Question 19

Two coherent sources have intensities I and 4I. The ratio of maximum to minimum intensity in the interference pattern is:

Accepted Answer

9 : 1. Amplitudes are in the ratio 1 : 2, so \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{2 + 1}{2 - 1}\right)^2 = 9.

Question 20

Two interfering waves have amplitudes in the ratio 5 : 3. The ratio of maximum to minimum intensity is:

Accepted Answer

16 : 1. Maximum amplitude = 8, minimum = 2, so the ratio of intensities is \left(\dfrac{8}{2}\right)^2 = 16 : 1.

Superposition & Interference — MH-CET Physics MCQs with Solutions

Questions with solutions