Question

An open pipe is suddenly closed at one end. As a result of which the fundamental frequency of the closed pipe is found to be less than that of open pipe by 150Hz. What is the fundamental frequency of the closed pipe?

Answer 1

Fundamental frequency of open organ pipe \[=\frac{v}{2l}\]                    Frequency of third harmonic of closed pipe \[=\frac{3V}{4l}\]                    \[\therefore \frac{3v}{4l}=100+\frac{v}{2l}\]\[\Rightarrow \frac{3v}{4l}-\frac{2v}{4l}=\frac{v}{4l}=100\]\[\Rightarrow \frac{V}{2l}=200\,Hz.\]