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 calculated using the formula:\[f = \frac{v}{\lambda},\]where \( v \) represents the speed of sound and \( \lambda \) denotes the wavelength. In the fundamental mode of an open pipe, the wavelength is given by:\[\lambda = 2L \quad \text{(corresponding to a complete wave pattern)}.\]Substituting this into the frequency formula yields:\[f = \frac{v}{2L}.\]Key Points:\begin{itemize} \item Open pipes exhibit standing waves with antinodes at both extremities. \item The fundamental frequency in an open pipe is characterized by a single node positioned centrally, flanked by antinodes at each open end.\end{itemize}---