Two sound waves each of wavelength $\lambda$ and having the same amplitude $A$ from two sources $S_1$ and $S_2$ interfere at a point $P$. If the path difference $S_2P - S_1P = \lambda/3$,then the amplitude of the resultant wave at point $P$ will be $[\cos(120^{\circ}) = -0.5]$.

Write the equation of displacement of the resultant wave for two superposed waves with an initial phase difference.

If $y_1 = 5 \text{ mm} \sin(\pi t)$ is the equation of oscillation of source $S_1$ and $y_2 = 5 \text{ mm} \sin(\pi t + \pi/6)$ is that of $S_2$,and it takes $1 \text{ s}$ and $0.5 \text{ s}$ for the transverse waves to reach point $A$ from sources $S_1$ and $S_2$ respectively,then the resulting amplitude at point $A$ is .... $\text{mm}$.

Obtain the resultant wave of more than two wave functions by representing the superposition principle mathematically.

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

Explain the superposition principle for waves forming in calm water.