Two waves of same frequency and intensity superimpose with each other in opposite phases,then after superposition the

Two waves $y_1 = A_1 \sin(\omega t - \beta_1)$ and $y_2 = A_2 \sin(\omega t - \beta_2)$ superimpose to form a resultant wave whose amplitude is:

$A$ 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 ... $cm$.

Two identical coherent sound sources $R$ and $S$ with frequency $f$ are $5 \,m$ apart. An observer standing equidistant from the sources at a perpendicular distance of $12 \,m$ from the line $RS$ hears maximum sound intensity. When the observer moves parallel to the line $RS$ to a position directly in front of one of the sources,the sound intensity is a minimum. $A$ possible value of $f$ is close to ............ $Hz$ (the speed of sound is $330 \,m/s$).

Two waves of equal amplitude and frequency interfere with each other. The ratio of intensity when the two waves arrive in phase to that when they arrive $90^{\circ}$ out of phase is:

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