First slide

Standing waves

Question

An organ pipe of length L is open at one end and closed at other end. The wavelengths of the three lowest resonating frequencies that can be produced by this pipe are

Moderate

A

4L, 2L, L
B

2L, L, $\frac{L}{2}$
C

2L, L, $\frac{2 L}{3}$
D

4L, $\frac{4 L}{3}$ , $\frac{4 L}{5}$

Solution

$L = (2 n - 1) \frac{λ}{4}$
$λ = \frac{4 L}{(2 n - 1)} \Rightarrow λ_{1} = \frac{4 L}{2 (1) - 1} = 4 L;$
$λ_{2} = \frac{4 L}{4 - 1} = \frac{4 L}{3} and λ_{3} = \frac{4 L}{6 - 1} = \frac{4 L}{5}$

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