Two identical sinusoidal waves are moving in the same direction along a stretched string and interfere with each other. The phase difference between them is $120^{\circ}$. The amplitudes of both the waves are the same. If the amplitude of the resultant wave due to interference is $2 \,mm$, the amplitude of each wave is:

The displacement of an elastic wave is given by the function: $y = 3\, \sin\, \omega t + 4\, \cos\, \omega t$,where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is ...... $cm$.

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 have intensities $x$ and $y$. If the time difference between them is $3T/2$,what is the resultant intensity?

Two sound waves having intensities $I$ and $4I$ interfere to produce an interference pattern. The phase difference between the waves is $\pi / 2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is (in $I$)

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times the amplitude of individual motions. The phase difference between the two motions is $.....( ^{\circ)}$