The superposition takes place between two waves of frequency $f$ and amplitude $a$. The total intensity is directly proportional to

$A$ sound wave of wavelength $32 \ cm$ enters the tube at $S$ as shown in the figure. Then the smallest radius $r$ so that a minimum of sound is heard at detector $D$ is ... $cm$.

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

Two loudspeakers $L_1$ and $L_2$,driven by a common oscillator and amplifier,are arranged as shown. The frequency of the oscillator is gradually increased from zero,and the detector at $D$ records a series of maxima and minima. If the speed of sound is $330 \, m/s$,then the frequency at which the first maximum is observed is .... $Hz$.

Two sound waves of intensity $2 \, W/m^2$ and $3 \, W/m^2$ meet at a point to produce a resultant intensity $5 \, W/m^2$. The phase difference between the two waves is ......

Two sinusoidal waves given below are superposed:
$y_1 = A \sin \left(kx - \omega t + \frac{\pi}{6}\right), \quad y_2 = A \sin \left(kx - \omega t - \frac{\pi}{6}\right)$
The equation of the resultant wave is: