What is the path difference for destructive interference?

The resultant amplitude of the interference of two waves $y_1 = 4 \sin \omega t$ and $y_2 = 3 \sin (\omega t + \frac{\pi}{3})$ is:

Two coherent sources have an intensity ratio of $100 : 1$ and are used to obtain the phenomenon of interference. What is the ratio of the maximum to the minimum intensity?

Two light beams of intensities $I$ and $4I$ produce an interference pattern on a screen. If the phase difference between them at point $A$ is $\pi/2$ and at point $B$ is $2\pi$,find the difference between the resultant intensities at points $A$ and $B$.

Two coherent plane light waves of equal amplitude make a small angle $\alpha (\alpha \ll 1)$ with each other. They fall almost normally on a screen. If $\lambda$ is the wavelength of the light waves,the fringe width $\Delta x$ of the interference pattern of the two sets of waves on the screen is:

The essential condition for obtaining a sustained interference pattern is that the two sources must . . . . . .