Question

The fundamental frequency '\(n\)' of the tuning fork is 288 Hz, it will not resonate with the frequency

• A. \(288\) Hz
• B. \(576\) Hz
• C. \(844\) Hz
• D. \(864\) Hz

Hint:

A fork resonates with its fundamental and its integer multiples. 844 is not a multiple of 288.

Answer 1

The Correct Option is C

Step 1: List the harmonic series:
$n = 288$, $2n = 576$, $3n = 864$, $4n = 1152$, and so on.

Step 2: Compare:
288, 576 and 864 appear in the list. 844 falls between $2n$ and $3n$ but does not match either, so it is missing.

Step 3: Conclusion:
Resonance needs a matching harmonic, so only 844 Hz fails.

Step 4: Why 844 Hz is not an overtone:
The 2nd and 3rd harmonics of 288 Hz are 576 Hz and 864 Hz. The number 844 lies between them, 20 Hz below the third harmonic, so no mode of the fork matches it and it cannot drive resonance.

Final Answer:
Option (C). \[ \boxed{844\text{ Hz (C)}} \]