Three harmonic waves having equal frequency $v$ and same intensity $I_{0}$,have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed,the intensity of the resultant wave is close to

Two waves represented by $y_1 = 10 \sin(200\pi t)$ and $y_2 = 20 \sin(200\pi t + \pi/2)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is:

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at point $D$ where a detector is placed. The maximum value of $\lambda$ to produce a minima at $D$ is given by

The resultant amplitude due to the superposition of two waves $y_1 = 5 \sin (\omega t - kx)$ and $y_2 = -5 \cos (\omega t - kx - 150^{\circ})$ is:

Two waves are represented by $y_1 = a \sin(\omega t + \frac{\pi}{6})$ and $y_2 = a \cos(\omega t)$. What will be their resultant amplitude?

Out of the given four waves $(1), (2), (3)$ and $(4)$:
$y = a \sin(kx + \omega t)$ ......$(1)$
$y = a \sin(\omega t - kx)$ ......$(2)$
$y = a \cos(\omega t - kx)$ ......$(3)$
$y = a \cos(kx + \omega t)$ ......$(4)$
emitted by four different sources $S_1, S_2, S_3$ and $S_4$ respectively,interference phenomena would be observed in space under appropriate conditions when: