Physics Wave Optics

A sound source S is moving along a straight track with speed v, and is emitting sound of frequency v? (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by:
(t? represents the instant when the distance between the source and observer is minimum)

Two coherent sources of sound, $S_1$ ${}_{}$ and $S_2$ ${}_{}$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$ $$ , in phase. $S_1$ ${}_{}$ and ${\mathrm{S}}_2$ ${}_{}$ are placed $1.5\mathrm{m}$ $$ apart (see fig). A listener located at $\mathrm{L}$ $$ , directly in front of $S_2$ ${}_{}$ finds that the intensity is at a minimum when he is $2\mathrm{m}$ $$ away from ${\mathrm{S}}_2$ ${}_{}$ . The listener moves away from $S_1$ ${}_{}$ , keeping his distance from $S_2$ ${}_{}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ $$ from ${}_{}$ $S_1$ . Then, $d$ $$ is:

Visible light of wavelength $6000*{10}^{-8}\mathrm{c}\mathrm{m}$ ${}^{}$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at ${60}^{?}$ ${}^{}$ from the central maximum. If the first minimum is produced at ${\theta }_1$ ${}_{}$ then ${\theta }_1$ ${}_{}$ is close to:

In a Young's double slit experiment, the separation between the slits is $0.15\mathrm{m}\mathrm{m}$ . In the experiment, a source of light of wavelength $589\mathrm{n}\mathrm{m}$ is used and the interference pattern is observed on a screen kept $1.5\mathrm{m}$  away. The separation between the successive bright fringes on the screen is:

A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $10\mathrm{\%}$ $$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is ‘x’ nm. The value of ‘x’ to the nearest integer is----------.

Red light differs from blue light as they have:

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is _____ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = 6000 Å]

In Young's double slit experiment, if the source of light changes from orange to blue then:

The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given µ? = 1)