If $y_1 = 5 \text{ mm} \sin(\pi t)$ is the equation of oscillation of source $S_1$ and $y_2 = 5 \text{ mm} \sin(\pi t + \pi/6)$ is that of $S_2$,and it takes $1 \text{ s}$ and $0.5 \text{ s}$ for the transverse waves to reach point $A$ from sources $S_1$ and $S_2$ respectively,then the resulting amplitude at point $A$ is .... $\text{mm}$.

$A$ 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 ... $cm$.

If the phase difference between two waves is $2\pi$ during superposition,then the resultant amplitude is

The displacement equations of two interfering waves are given by
$y_1 = 10 \sin \left(\omega t + \frac{\pi}{3}\right) \text{ cm}$
$y_2 = 5[\sin (\omega t) + \sqrt{3} \cos \omega t] \text{ cm}$ respectively.
The amplitude of the resultant wave is $............. \text{ cm}$.

Two sound waves (expressed in $CGS$ units) given by $y_1 = 0.3 \sin \frac{2\pi}{\lambda}(vt - x)$ and $y_2 = 0.4 \sin \frac{2\pi}{\lambda}(vt - x + \theta)$ interfere. The resultant amplitude at a place where phase difference is $\pi/2$ will be .... $cm$.

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 $330 \,m/s$).