MHT CET · Physics · Oscillations
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
- A 3 A
- B 4 A
- C 2 A
- D \(1 \mathrm{~A}\)
Answer & Solution
Correct Answer
(A) 3 A
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned}
& n_X^2 A_X^2=n_Y^2 A_Y^2 \\
& \Rightarrow n A=\frac{n}{3} A_Y ...(given)\\
\therefore \quad & \frac{A_Y}{A}=\frac{n}{n / 3} .\\
& \Rightarrow A_Y=3 A
\end{aligned}\)
\(E=\frac{1}{2} m \omega^2 A^2 \text { But }, \omega=2 \pi n\)
\(\therefore \quad \mathrm{E} \propto \mathrm{n}^2 \mathrm{~A}^2\)
As the energies are equal,
\(\begin{aligned}
& n_X^2 A_X^2=n_Y^2 A_Y^2 \\
& \Rightarrow n A=\frac{n}{3} A_Y ...(given)\\
\therefore \quad & \frac{A_Y}{A}=\frac{n}{n / 3} .\\
& \Rightarrow A_Y=3 A
\end{aligned}\)
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