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. \(A\)
• B. \(2A\)
• C. \(4A\)
• D. \(8A\)

Hint:

Wave energy is proportional to the square of the amplitude times the square of the frequency.

Answer 1

The Correct Option is C

Step 1: Define energy.
Energy $\propto (\text{frequency} \times \text{amplitude})^2$.

Step 2: Compare.
So $f_PA_P = f_QA_Q$, which gives $nA = (n/4)A_Q$.

Step 3: Result.
$A_Q = 4A$. A lower frequency has to be balanced by a larger amplitude.

Final Answer:
Option (C). \[ \boxed{4A} \]