Overtone Frequencies in Pipes – Rankers Physics
Topic: Waves
Subtopic: Standing Wave in String and Organ Pipe

Overtone Frequencies in Pipes

The frequency of the first overtone of a closed pipe of length \(L_1\), is equal to that of the first overtone of an open pipe of length \(L_2\). The ratio of their lengths \((L_1 : L_2)\) is:
2 : 3
4 : 5
3 : 5
3 : 4

Solution:

The first overtone of a closed pipe of length \(L_1\) has frequency \(f_{c,1} = \frac{3v}{4L_1}\) and that of an open pipe of length \(L_2\) is \(f_{o,1} = \frac{v}{L_2}\). Equating the two frequencies gives \(\frac{3v}{4L_1} = \frac{v}{L_2}\), which simplifies to \(\frac{L_1}{L_2} = \frac{3}{4}\).

Leave a Reply

Your email address will not be published. Required fields are marked *