First slide

Standing waves

Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

Moderate

A

$\frac{L}{2}$
B

4L
C

L
D

2L

Solution

For second overtone (3rd harmonic) in open organ pipe,
$\frac{3 λ}{2} = l_{0} \Rightarrow λ = \frac{2 l_{0}}{3}$
For first overtone (3'd harmonic) in closed organ pipe,
$\frac{3 λ}{4} = l_{C} \Rightarrow λ = \frac{4 l_{c}}{3} = \frac{4 L}{3}$
$So, \frac{2 l_{0}}{3} = \frac{4 L}{3} \Rightarrow l_{0} = 2 L$

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