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 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 waves have equations $x_1 = a \sin(\omega t + \phi_1)$ and $x_2 = a \sin(\omega t + \phi_2)$. If the frequency and amplitude of the resultant wave remain equal to those of the superimposing waves,then the phase difference between them is:

Obtain the equation of resultant displacement of two progressive harmonic waves on a stretched string.

The equations of two waves are given by
$y_{1}=5 \sin 2 \pi(x-v t) \, cm$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \, cm$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$.

When two sound waves having amplitude $3$ and $5$ units are superimposed,then the ratio of maximum to minimum intensity of the wave produced is: