Physics - Sound Wave Question with Solution | TestHub

Let $L$ be the original length of the closed pipe.

The fundamental frequency of a closed pipe is given by $n=\frac{v}{4L}=400$ Hz.

When $\frac{1}{3}$ of the pipe is filled with water, the water acts as the new closed end. The new length of the air column is $L^{\prime }=L-\frac{L}{3}=\frac{2L}{3}$.

The new fundamental frequency is $n^{\prime }=\frac{v}{4L^{\prime }}=\frac{v}{4\left(\frac{2L}{3}\right)}=\frac{3}{2}\left(\frac{v}{4L}\right)$.

Substituting the value of $\frac{v}{4L}$, we get $n^{\prime }=\frac{3}{2}\times 400=600$ Hz.

For a closed pipe, the first overtone is the third harmonic, which is $3n^{\prime }$.

Frequency of the first overtone $=3\times 600=1800$ Hz.

Answer: 1800 Hz