Questions: Multiple Choice Question O f = 4/L O f = 2/L O f = 4L A1 in pipe open both ends of length L and sound wave speed v. What is the resonant frequency of the standing wave? Read About the Concept Need help? Review these concepts

Solution Steps

We are given a pipe open at both ends with length \( L \) and a sound wave speed \( v \). We need to determine the resonant frequency of the standing wave in this pipe.

For a pipe open at both ends, the resonant frequencies occur at harmonics of the fundamental frequency. The fundamental frequency \( f_1 \) is given by:

\[ f_1 = \frac{v}{2L} \]

This is because the pipe supports a standing wave with a wavelength \( \lambda = 2L \) for the fundamental frequency.

The options provided are:

• \( f = \frac{4}{L} \)
• \( f = \frac{2}{L} \)
• \( f = 4L \)

We need to compare these with the expression for the fundamental frequency \( f_1 = \frac{v}{2L} \).

The correct expression for the fundamental frequency in terms of \( L \) and \( v \) is \( f = \frac{v}{2L} \). None of the options directly match this expression. However, if we assume \( v = 2 \), then:

\[ f = \frac{2}{L} \]

This matches the second option.

Final Answer