Question

parta
an pipe of length l that is open at both ends is resonating at its fundamental frequency. which statement about the sound is correct?
the wavelength is 2l and there is a displacement antinode at the pipes midpoint.
the wavelength is l and there is a displacement node at the pipes midpoint.
the wavelength is l and there is a displacement antinode at the pipes midpoint.
the wavelength is 2l and there is a displacement node at the pipes midpoint.

Explanation:

Step1: Recall the formula for wavelength in open - open pipes

For a pipe open at both ends, the fundamental frequency \(f_1\) has the relation \(L = \frac{n\lambda}{2}\), where \(n = 1\) for the fundamental frequency. So, \(\lambda=2L\).

Step2: Determine the nature of the point at the mid - point

In a pipe open at both ends, the open ends are displacement antinodes. For the fundamental mode (\(n = 1\)), the mid - point of the pipe (since \(L=\frac{\lambda}{2}\)) is also a displacement antinode.

Answer:

The wavelength is \(2L\) and there is a displacement antinode at the pipe's midpoint.