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 $...... \, {mm}$.

The displacement of an elastic wave is given by the function: $y = 3\, \sin\, \omega t + 4\, \cos\, \omega t$,where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is ...... $cm$.

The similarity between sound and light waves is:

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 $\sqrt{5} = 2.23$)

Two identical waves $1$ and $2$,each of intensity $I_0$,are superimposed. The resulting intensity is:

Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive $90^{\circ}$ out of phase is $\left[\cos \frac{\pi}{2}=0\right]$