Two generators $S_1$ and $S_2$ produce water wave 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 $P$ ?
Medium
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$\Delta x=\frac{\lambda}{2}$ $\Delta \mathrm{x}$ path difference
$\Delta \phi=\mathrm{k} \Delta \mathrm{x}$
$=\frac{2 \pi}{\lambda} \times \frac{\lambda}{2}=\pi$
Hence destructive interference will occur at point $P.$
$A_{\text {resultant }}=\sqrt{(2 a)^{2}+a^{2}-4 a^{2}}=a$
It will remain constant with time.
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