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(C) For a point source in a non-absorbing medium,the intensity $I$ at a distance $r$ is given by $I = \frac{P}{4\pi r^2}$,where $P$ is the power of th

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$25 : 9$

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(C) For a point source in a non-absorbing medium,the intensity $I$ at a distance $r$ is given by $I = \frac{P}{4\pi r^2}$,where $P$ is the power of the source.Since $I \propto \frac{1}{r^2}$ and intensity is proportional to the square of the amplitude $(I \propto A^2)$,we have $A^2 \propto \frac{1}{r^2}$,which implies $A \propto \frac{1}{r}$.Therefore,the ratio of amplitudes at points $P$ and $Q$ is $\frac{A_P}{A_Q} = \frac{r_Q}{r_P}$.Given $r_P = 9 \ m$ and $r_Q = 25 \ m$,we get $\frac{A_P}{A_Q} = \frac{25}{9}$.Thus,the ratio is $25 : 9$.

$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9 \ m$ and $25 \ m$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

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