Question

The lowest frequency of the air column in an open pipe of length \( L \) is \( v \) (velocity of sound in air)

• A. \( \frac{v}{2L} \)
• B. \( \frac{v}{4L} \)
• C. \( \frac{v}{L} \)
• D. \( \frac{v}{8L} \)
• E. \( \frac{2v}{L} \)

Hint:

For open pipes, the fundamental frequency corresponds to the case where the pipe has one node at each end and a maximum displacement in the middle.

Answer 1

The Correct Option is A

In an open pipe, the lowest frequency (fundamental frequency) corresponds to the situation where the pipe behaves as a resonator with the first harmonic. The first harmonic is formed when the pipe has a node at both ends, and the wavelength \( \lambda \) is twice the length of the pipe: \[ \lambda = 2L \] The speed of sound \( v \) is related to the frequency \( f \) and wavelength \( \lambda \) by the equation: \[ v = f \lambda \] Substitute \( \lambda = 2L \): \[ v = f \cdot 2L \] Solving for the frequency: \[ f = \frac{v}{2L} \] Hence, the correct answer is (A).