The displacements of two interfering light waves are given by $y_1 = 4 \sin \omega t$ and $y_2 = 3 \sin (\omega t + \frac{\pi}{2})$. What is the amplitude of the resultant wave?

Two waves of intensity ratio $1:9$ cross each other at a point. The resultant intensities at the point are $I_1$ when the waves are incoherent and $I_2$ when the waves are coherent with a phase difference of $60^{\circ}$. If $\frac{I_1}{I_2} = \frac{10}{x}$,then $x = . . . . . . . . . . .$

To demonstrate the phenomenon of interference,we require two sources which emit radiation:

Two identical coherent sources are placed on a diameter of a circle of radius $R$ at a separation $x (x << R)$,symmetrically about the center of the circle. The sources emit waves of identical wavelength $\lambda$. Find the number of points on the circle with maximum intensity,given $x = 5 \lambda$.

When two light waves of equal intensity superimpose, the maximum intensity obtained is $I$. If the intensity of one of the waves is quadrupled, then the maximum intensity obtained is

The interference pattern is obtained with two coherent light sources of intensity ratio $4:1$. If the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is $\frac{5}{x}$,then the value of $x$ will be equal to: