Question

A pipe open at both ends has a frequency \(f\) in air. The pipe is dipped vertically in water, so that its \((1/3)\) part of its length is in water. The fundamental frequency of the air column is now \(xf\), the value of \(x\) is

• A. \(\frac{1}{2}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{3}{2}\)
• D. \(1\)

Hint:

Once one third is under water the pipe behaves as a closed pipe of length two thirds of the original.

Answer 1

The Correct Option is B

Step 1: Open pipe
$f=\frac{v}{2L}$.

Step 2: Closed pipe formula
For a closed pipe of length $l$, $f'=\frac{v}{4l}$ with $l=\frac{2L}{3}$.

Step 3: Ratio
$f'=\frac{3v}{8L}=\frac{3}{4}\cdot\frac{v}{2L}=\frac{3}{4}f$, so option (B) is correct.

Final Answer:
The new fundamental is three-quarters of the original. \[ \boxed{\text{(B) }\dfrac{3}{4}} \]