Question

An open-open organ pipe is 78.0 cm long. An open-closed pipe has a fundamental frequency equal to the third harmonic of the open-open pipe. How long is the open-closed pipe?

Short answer

The open-close pipe is 13.0 cm long.

Step-by-step solution

The concept of frequency 

In physics, the term 'frequency' refers to the wave that moves from one fixed point to another fixed point.

The frequency of the open-closed tube with the equation 

The frequency of the open-closed tube is $f=\frac{v}{4L}$

The third harmonic of the tube is $f=\frac{3v}{2L_0}$

The expression of the length or L is$$\begin{gathered} \frac{3v}{2L_0}=\frac{v}{4L}\Rightarrow \boxed{L=\frac{1}{6}{L}_0} \\ L=\frac{78}{6}=\boxed{13cm} \end{gathered}$$