1. Fundamental frequency of the original pipe

A pipe open at both ends and of length $L$ has fundamental frequency

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

where $v$ is the speed of sound in air.

2. After dipping half the pipe in water

Since half the pipe is submerged, the lower half gets filled with water. So the remaining air column has length

$L' = \frac{L}{2}$

Now the lower end of the air column is in contact with water, so it behaves like a closed end, while the upper end remains open.

Thus the pipe now acts like a closed pipe of length $L/2$.

3. Fundamental frequency of a closed pipe

For a pipe closed at one end and open at the other, the fundamental frequency is

$f' = \frac{v}{4L'}$

Substitute $L' = L/2$:

$f' = \frac{v}{4(L/2)} = \frac{v}{2L}$

But originally,

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

So,

$f' = f$

4. Check options

• A: $2f$ — incorrect
• B: $f$ — correct
• C: $\dfrac{f}{2}$ — incorrect
• D: $\dfrac{3f}{4}$ — incorrect

Hence, the correct answer is B.