First slide

Standing waves

Question

For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz. The speed of sound in air is 340 m/s. The pipe is a

Difficult

A

closed pipe of length 1m
B

closed pipe of length 2m
C

open pipe of length 1m
D

open pipe of length 2m

Solution

$425 = 5 \times 85 595 = 7 \times 85$ and $765 = 9 \times 85$
For a closed pipe, $f = n \frac{V}{4 l}$ where n = odd numbers
$∴ \frac{V}{4 l} = 85 \Rightarrow l = \frac{340}{4 \times 85} m = 1 m$

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