Interference General Case

Q. Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is

1. \N
2. A
3. 2A
4. between 0 and 2A

Q. Two identical speakers, emit sound waves of frequency ${10}^3\text{Hz}$ uniformly in all directions.
The audio output of each speaker is $\frac{9\pi }{10}\text{mW}$. A point $P$ is at a distance of $3\text{m}$ from $S_1$ and $5\text{m}$ from $S_2$. Resultant intensity of sound at $P$ is

1. $34\mu W/m^2,$ if the sources are incoherent.
2. $4\mu W/m^2,$ if the sources are coherent but out of phase.
3. $25\mu W/m^2,$ if $S_1$ is switched off.
4. $64\mu W/m^2,$ if the sources are coherent and in phase.

Q.

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of sources can be varied continuously. Complete destructive refraction is observed for $\lambda =5000\dot{A}$ and $\lambda =7000\dot{A}$ and for no other wavelength in between. If $\mu$ of oil is 1.3 and that of glass is 1.5, the thickness of the film will be

1. $6.378\times {10}^{-5}cm$
2. $5.7\times {10}^{-5}cm$
3. $4\times {10}^{-5}cm$
4. $2.8\times {10}^{-5}cm$