Question:
A musical instrument P produces sound waves of frequency 'n' and amplitude 'A'. Another musical instrument Q produces sound waves of frequency n/4. The waves produced by P and Q have equal energies. The amplitude of waves produced by Q will be
A musical instrument P produces sound waves of frequency 'n' and amplitude 'A'. Another musical instrument Q produces sound waves of frequency n/4. The waves produced by P and Q have equal energies. The amplitude of waves produced by Q will be
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Wave energy is proportional to the square of the amplitude times the square of the frequency.
Updated On: Oct 1, 2026
- \(A\)
- \(2A\)
- \(4A\)
- \(8A\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
The energy of a wave per unit volume depends on \(\omega^2A^2\), so \(E\propto f^2A^2\).
Step 2: Set the energies equal.
\[ n^2A^2 = \left(\frac{n}{4}\right)^2A_Q^2 \]
Step 3: Solve.
\[ A_Q^2 = 16A^2 \Rightarrow A_Q = 4A \]
Step 4: Check the options.
\(A\) would be right only if the frequencies were equal. \(2A\) and \(8A\) do not satisfy the equation.
Final Answer:
The amplitude of Q is \(4A\), option (C). \[ \boxed{4A} \]
The energy of a wave per unit volume depends on \(\omega^2A^2\), so \(E\propto f^2A^2\).
Step 2: Set the energies equal.
\[ n^2A^2 = \left(\frac{n}{4}\right)^2A_Q^2 \]
Step 3: Solve.
\[ A_Q^2 = 16A^2 \Rightarrow A_Q = 4A \]
Step 4: Check the options.
\(A\) would be right only if the frequencies were equal. \(2A\) and \(8A\) do not satisfy the equation.
Final Answer:
The amplitude of Q is \(4A\), option (C). \[ \boxed{4A} \]
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