Question

Resonance is produced between a tuning fork and a resonance column tube with its upper end open and lower end closed by a water surface. If the frequency of the tuning fork is $800\text{ Hz}$, and the first two resonances are observed at lengths $75\text{ cm}$ and $325\text{ cm}$, find the length at which the third resonance occurs and the speed of sound.

• A. $43.10\text{ cm}$ and $340\text{ m s}^{-1}$
• B. $31.25\text{ cm}$ and $330\text{ m s}^{-1}$
• C. $62.60\text{ cm}$ and $335\text{ m s}^{-1}$
• D. $52.75\text{ cm}$ and $344\text{ m s}^{-1}$

Hint:

For a closed pipe system, the gap between consecutive positions is constant. Since the gap between the first two values is $21.5\text{ cm}$, simply add $21.5$ to the second length to get the third position instantly: $31.25 + 21.5 = 52.75\text{ cm}$. This leaves only Option (D) as a viable choice!

Answer 1

The Correct Option is D