The resultant amplitude due to the superposition of two waves $y_1 = 5 \sin (\omega t - kx)$ and $y_2 = -5 \cos (\omega t - kx - 150^{\circ})$ is:

Four harmonic waves of equal frequencies and equal intensities $I_0$ have phase angles $0, \pi / 3, 2 \pi / 3$ and $\pi$. When they are superposed,the intensity of the resulting wave is $nI_0$. The value of $n$ is

When two sound waves with a phase difference of $\pi / 2$,and each having amplitude $A$ and frequency $\omega$,are superimposed on each other,then the maximum amplitude and frequency of the resultant wave is:

Write the equation of displacement of the resultant wave for two superposed waves with an initial phase difference.

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 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 $y_2 = A \cos[k(x + vt) + \phi]$.