Physics - Wave on String Question with Solution | TestHub

Total length of the pipe, $L_0=1.5\text{ m}$.

When the pipe is dipped in water at one end, it behaves as a pipe closed at one end. Let the length of the air column be $L$.

The frequency of the $2^{\text{nd}}$ overtone for a pipe closed at one end is the $5^{\text{th}}$ harmonic, given by:

$n_2=\frac{5v}{4L}$

Given $n_2=330\text{ Hz}$ and $v=330\text{ m/s}$, substituting these values:

$330=\frac{5\times 330}{4L}$

$4L=5\Rightarrow L=1.25\text{ m}$

The length of the pipe immersed in water is the total length minus the length of the air column:

Length immersed $=L_0-L=1.5-1.25=0.25\text{ m}$

Answer: 0.25 m