A musical instrument ' P ' produces sound waves of frequency ' \(n\) ' and amplitude ' \(A\) '. Another musical instrument ' Q ' produces sound waves of frequency \(\frac{n}{4}\). The waves produced by ' \(P\) ' and ' \(Q\) ' have equal energies. If the amplitude of waves produced by ' P ' is ' \(\mathrm{A}_{\mathrm{P}}\) ', the amplitude of waves produced by ' Q ' will be

Energy of oscillations is given by
\(E=\frac{1}{2} m \omega^2 A^2=\frac{1}{2} m(2 \pi n)^2 A^2\)
\(\therefore \quad E \propto \mathrm{n}^2 \mathrm{~A}^2\)
As the energies are equal,
\(\begin{array}{ll}
& \mathrm{n}_1^2 \mathrm{~A}_1^2=\mathrm{n}_2^2 \mathrm{~A}_2^2 \Rightarrow \mathrm{n}_1 \mathrm{~A}_1=\mathrm{n}_2 \mathrm{~A}_2 \\
\therefore \quad & \frac{\mathrm{~A}_2}{\mathrm{~A}_1}=\frac{\mathrm{n}_1}{\mathrm{n}_2}=\frac{\mathrm{n}}{\mathrm{n} / 4}=4 \\
\therefore \quad & \mathrm{~A}_2=4 \mathrm{~A}_1 \quad \\
\therefore & \left.\mathrm{~A}=4 \mathrm{~A}_{\mathrm{p}} \quad \text {... (given, } \mathrm{A}_1=A, \mathrm{~A}_2=\mathrm{A}_{\mathrm{p}}\right)
\end{array}\)