Two generators $S_1$ and $S_2$ produce water waves of equal frequency. $A$ point $P$ is located such that $(S_1P - S_2P)$ is equal to half a wavelength. When operated alone,$S_1$ produces an oscillation of amplitude $2a$ at $P$,while $S_2$ produces an oscillation of amplitude $a$. If the generators are operated in phase,which graph correctly shows the resultant oscillation at $P$?

Two pulses travel in mutually opposite directions in a string with a speed of $2.5 \ cm/s$ as shown in the figure. Initially,the pulses are $10 \ cm$ apart. What will be the state of the string after two seconds?

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

The amplitude of the resultant wave produced by the superposition of two waves $y_1 = A_1 \sin(wt - \beta_1)$ and $y_2 = A_2 \sin(wt - \beta_2)$ is:

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 the same amplitude $A$ and the same frequency $\omega$. If the phase difference between them is $\pi / 2$,what are the resultant amplitude and the resultant frequency when they superimpose at a point?