Two waves represented by $y_1 = 10 \sin(200\pi t)$ and $y_2 = 20 \sin(200\pi t + \pi/2)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is:

Explain the superposition principle for waves forming in calm water.

Two waves are propagating along a taut string that coincides with the $x$-axis. The first wave has the wave function $y_1 = A \cos[k(x - vt)]$ and the second has the wave function $y_2 = A \cos[k(x + vt) + \phi]$.

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 coherent sources of sound,$S_{1}$ and $S_{2}$,produce sound waves of the same wavelength,$\lambda = 1\, m$,in phase. $S_{1}$ and $S_{2}$ are placed $1.5\, m$ apart (see figure). $A$ listener,located at $L$,directly in front of $S_{2}$,finds that the intensity is at a minimum when he is $2\, m$ away from $S_{2}$. The listener moves away from $S_{1}$,keeping his distance from $S_{2}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_{1}$. Then,$d$ is $......\, m$.

Two waves represented by $y_1 = a \sin \frac{2\pi}{\lambda} (vt - x)$ and $y_2 = a \cos \frac{2\pi}{\lambda} (vt - x)$ are superposed. The resultant wave has an amplitude equal to