A musical instrument X produces sound waves of frequency n and amplitude A . Another musical instrument $Y$…
A musical instrument X produces sound waves of frequency n and amplitude A . Another musical instrument $Y$ produces sound waves of frequency $\frac{\mathrm{n}}{3}$. The waves produced by x and y have equal energies. The amplitude of waves produced by Y will be
3 A
4 A
2 A
$1 \mathrm{~A}$
Solution
Energy of oscillations is given by
$E=\frac{1}{2} m \omega^2 A^2 \text { But }, \omega=2 \pi n$
$\therefore \quad \mathrm{E} \propto \mathrm{n}^2 \mathrm{~A}^2$
As the energies are equal,
$\begin{aligned}
& n_X^2 A_X^2=n_Y^2 A_Y^2 \\
& \Rightarrow n A=\frac{n}{3} A_Y ...(given)\\
\therefore \quad & \frac{A_Y}{A}=\frac{n}{n / 3} .\\
& \Rightarrow A_Y=3 A
\end{aligned}$