When two sound waves with a phase difference of $\pi / 2$,and each having amplitude $A$ and frequency $\omega$,are superimposed on each other,then the maximum amplitude and frequency of the resultant wave is:

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

Three coherent waves of equal frequencies having amplitudes $10 \, \mu m$,$4 \, \mu m$,and $7 \, \mu m$ respectively,arrive at a given point with successive phase differences of $\pi / 2$. The amplitude of the resulting wave in $\mu m$ is given by

When two progressive waves $y_1=4 \sin (2 x-6 t)$ and $y_2=3 \sin \left(2 x-6 t-\frac{\pi}{2}\right)$ are superimposed,the amplitude of the resultant wave is

Two waves are propagating to point $P$ along a straight line,produced by two sources $A$ and $B$ of simple harmonic motion and equal frequency. The amplitude of every wave at $P$ is $a$. The phase of $A$ is ahead by $\frac{\pi}{3}$ compared to $B$,and the distance $AP$ is greater than $BP$ by $50 \ cm$. If the wavelength is $1 \ m$,what will be the resultant amplitude at point $P$?

Two generators $S_1$ and $S_2$ produce water waves of equal frequency. $A$ point $P$ is located such that $(S_1P - S_2P)$ is equal to half a wavelength. When operated alone,$S_1$ produces an oscillation of amplitude $2a$ at $P$,while $S_2$ produces an oscillation of amplitude $a$. If the generators are operated in phase,which graph correctly shows the resultant oscillation at $P$?