Question

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

• A. $\frac{f}{2}$
• B. $\frac{3f}{4}$
• C. $2f$
• D. $f$

Answer 1

The correct option is D $f$

For open end pipe in air, fundamental frequency

$f=\frac{V}{2L}$

For the pipe closed at one end (dipped in water), fundamental frequency

$f^{\prime }=\frac{V}{4L^{\prime }}$

$L^{\prime }=\frac{L}{2}$

$f^{\prime }=\frac{V}{2L}=f$