Physics - Wave on String Question with Solution | TestHub

The energy of a sound wave is directly proportional to the square of its frequency and the square of its amplitude.

$E\propto f^2{A}^2$

Given that the waves produced by P and Q have equal energies:

$E_P=E_Q$

$f_P^2{A}_P^2=f_Q^2{A}_Q^2$

Substituting the given values $f_P=n$, $A_P=A$, and $f_Q=\frac{n}{4}$:

$n^2{A}^2={\left(\frac{n}{4}\right)}^2{A}_Q^2$

$n^2{A}^2=\frac{n^2}{16}{A}_Q^2$

$A_Q^2=16A^2$

$A_Q=4A$

Answer: $4A$