Two pulses in a stretched string whose centres are initially $8 \ cm$ apart are moving towards each other as shown in the figure. The speed of each pulse is $2 \ cm/s$. After $2 \ seconds$,the total energy of the pulses will be

Equations of motion for two waves traveling in the same direction are given by $y_1 = 2a \sin(\omega t - kx)$ and $y_2 = 2a \sin(\omega t - kx - \theta)$. The resultant amplitude of the medium particle will be:

$A$ 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

Two waves are propagating along a taut string that coincides with the $x$-axis. The first wave has the wave function $y_1 = A \cos[k(x - vt)]$ and the second has the wave function $y_2 = A \cos[k(x + vt) + \phi]$.

$A$ sound wave of wavelength $32 \ cm$ enters the tube at $S$ as shown in the figure. Then the smallest radius $r$ so that a minimum of sound is heard at detector $D$ is ... $cm$.

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?