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Question

(B) The energy $E$ of a sound wave is proportional to the square of its amplitude $A$ and the square of its frequency $n$. Mathematically,$E \propto A

Vedclass · Accepted Answer

$4$

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(B) The energy $E$ of a sound wave is proportional to the square of its amplitude $A$ and the square of its frequency $n$. Mathematically,$E \propto A^2 n^2$.Since the energies of the waves produced by $P$ and $Q$ are equal,we have $E_P = E_Q$.This implies $A_P^2 n_P^2 = A_Q^2 n_Q^2$.Given $n_P = n$ and $n_Q = \frac{n}{4}$,we substitute these values into the equation:$A_P^2 n^2 = A_Q^2 (\frac{n}{4})^2$.$A_P^2 n^2 = A_Q^2 (\frac{n^2}{16})$.Dividing both sides by $n^2$,we get $A_P^2 = \frac{A_Q^2}{16}$.$A_Q^2 = 16 A_P^2$.Taking the square root of both sides,we get $A_Q = 4 A_P$.

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