Three waves of equal frequency having amplitudes $10 \,\mu m, 4 \,\mu m$ and $7 \,\mu m$ arrive at a given point with successive phase difference of $\frac{\pi}{2}$. The amplitude of the resulting wave in $\mu m$ is given by

If two waves represented by $y_1 = 4\sin \omega t$ and $y_2 = 3\sin (\omega t + \pi/3)$ interfere at a point,the amplitude of the resulting wave will be about

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

Four independent waves are represented by the following equations. Which of these equations represent the phenomenon of interference?
$Y_1 = a_1 \sin \omega t$
$Y_2 = a_2 \sin \omega t$
$Y_3 = a_3 \cos \omega t$
$Y_4 = a_4 \sin (\omega t + \frac{\pi}{3})$

$A$ 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 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 .... $cm$.