A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its l…

Question

A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

1. A. f/2
2. B. f (Correct answer)
3. C. 3f/2
4. D. 2f

Correct Answer

Option B — f

Detailed Solution & Explanation

The correct answer is $f$.

Key Points

• Open pipe (both ends open) of length $L$: $f=\dfrac{v}{2L}$.
• When dipped to half its length in water, the effective air column length is $\dfrac{L}{2}$ and it now behaves as a closed pipe (one end closed): $f'=\dfrac{v}{4(L/2)}=\dfrac{v}{2L}$.
• Therefore $f'=f$ — the fundamental frequency is unchanged.