Question

What is the fundamental frequency of an open organ pipe with length \( L \) and speed of sound \( v \)?

• A. \( \frac{v}{2L} \)
• B. \( \frac{v}{L} \)
• C. \( \frac{2v}{L} \)
• D. \( \frac{vL}{2} \)

Hint:

For an open pipe, the frequency increases with decreasing pipe length. The fundamental frequency is the lowest frequency.

Answer 1

The Correct Option is A

The fundamental frequency of an open organ pipe is determined by the formula: \[ f = \frac{v}{\lambda}, \] where \( v \) is the speed of sound and \( \lambda \) is the wavelength. For the fundamental mode of an open pipe: \[ \lambda = 2L \quad \text{(since the pipe supports a full wave)}. \] Substituting \( \lambda = 2L \): \[ f = \frac{v}{2L}. \] Explanation: \begin{itemize} \item In an open pipe, standing waves are formed with antinodes at both open ends. \item For the fundamental frequency, there is one node in the middle and two antinodes at the ends. \end{itemize} ---