Physics - Sound Wave Question with Solution | TestHub

Let $L$ be the original length of the closed pipe and $v$ be the speed of sound in air.

The fundamental frequency of the closed pipe is:

$n=\frac{v}{4L}=400\text{ Hz}$

When ${\frac{1}{3}}^{\text{rd}}$ of the pipe is filled with water, the new length of the air column is:

$L^{\prime }=L-\frac{L}{3}=\frac{2L}{3}$

The new fundamental frequency $n^{\prime }$ of the pipe is:

$n^{\prime }=\frac{v}{4L^{\prime }}=\frac{v}{4\left(\frac{2L}{3}\right)}=\frac{3}{2}\left(\frac{v}{4L}\right)$

Substituting $n=400\text{ Hz}$:

$n^{\prime }=\frac{3}{2}\times 400=600\text{ Hz}$

For a pipe closed at one end, the frequency of the $3^{\text{rd}}$ harmonic is $3$ times the fundamental frequency.

Frequency of $3^{\text{rd}}$ harmonic $=3n^{\prime }=3\times 600=1800\text{ Hz}$