The amplitude of the resultant wave produced by the superposition of two waves $y_1 = A_1 \sin(wt - \beta_1)$ and $y_2 = A_2 \sin(wt - \beta_2)$ is:

Two pulses travel in mutually opposite directions in a string with a speed of $2.5 \ cm/s$ as shown in the figure. Initially,the pulses are $10 \ cm$ apart. What will be the state of the string after two seconds?

The resultant amplitude of waves ${y_1} = a \sin \left( \omega t + \frac{\pi}{3} \right)$ and ${y_2} = a \sin \omega t$ is:

Two waves are superimposed whose ratio of intensities is $9: 1$. The ratio of maximum and minimum intensity is

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:

Sound waves are passing through two routes—one in a straight path and the other along a semicircular path of radius $r$—and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is $v$,then frequencies of resultant waves of maximum amplitude will be integral multiples of