When two light waves each of amplitude $A$ and having a phase difference of $\frac{\pi}{2}$ are superimposed,the amplitude of the resultant wave is:

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 $P$?

Two loudspeakers ($L_1$ and $L_2$) are placed with a separation of $10 \ m$, as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. $A$ voice recorder, initially at point $A$, at equidistance to both loudspeakers, is moved by $25 \ m$ along the line $AB$ while monitoring the audio signal. The measured signal was found to undergo $10$ cycles of minima and maxima during the movement. The frequency of the input signal is . . . . . . $Hz$. (Speed of sound in air is $324 \ m/s$ and $\sqrt{5} = 2.23$)

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

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 simultaneously passing through a string and their equations are:
${y}_{1} = {A}_{1} \sin {k}({x} - {vt}), {y}_{2} = {A}_{2} \sin {k}({x} - {vt} + {x}_{0}).$
Given amplitudes ${A}_{1} = 12 \, {mm}$ and ${A}_{2} = 5 \, {mm}$,${x}_{0} = 3.5 \, {cm}$,and wave number ${k} = 6.28 \, {cm}^{-1}$. The amplitude of the resulting wave will be $...... \, {mm}$.