Question

A pipe closed at one end produces a fundamental note of frequency 'v'. The pipe is cut into two pipes of equal lengths. The fundamental frequencies produced in the two pipes are ______.

Options

• \[\frac{v}{2}\], v

• v, 2v

• 2v, \[\frac{v}{2}\]

• 2v, 4v

Answer 1

A pipe closed at one end produces a fundamental note of frequency 'v'. The pipe is cut into two pipes of equal lengths. The fundamental frequencies produced in the two pipes are 2v, 4v.

Explanation:

For a pipe closed at one end, the fundamental frequency is given by \[\text{v}={\frac{\text{v}}{4\text{L}}}\]

When it is cut into two pipes of some length, we get one open pipe and one closed pipe each of length \[\frac{L}{2}\].

For open pipe: \[\text{v}_{1}={\frac{\text{v}}{2\left({\frac{\text{L}}{2}}\right)}}={\frac{\text{v}}{\text{L}}}=4\text{v}\]

For closed pipe: \[\text{v}_{2}={\frac{\text{v}}{4\left({\frac{\text{L}}{2}}\right)}}={\frac{\text{v}}{\text{2L}}}=2\text{v}\]