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The first three natural frequencies of an organ pipe are 126.0 Hz, 378.0 Hz, and 630.0 Hz. (a) Is the pipe open or closed? (b) Taking the temperature of the surrounding to be 25.0 C, find the length of the pipe.
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(a) Is the pipe open or closed?
Open Pipes have harmonics N = 1,2,3,4,5...
Closed Pipes have harmonics N = 1,3,5,7... (odd numbers)

378.0 Hz / 126.0 Hz = 3.
Thus this pipe is a Closed Pipe.

Double check yourself.
630.0 Hz / 126.0 Hz = 5.

Closed Pipe checks out.

(b) Taking the temperature of the surrounding to be 25.0 C, find the length of the pipe.
for a closed pipe:
f_n = V_s* n / (4*L).

Setting n = 1,
f_1 = V_s /(4*L).

Solving for L,
L = V_s / (4 *f_1)
= 350 m/s / ( 4 * 126 Hz)
= 0.675 m

L = 0.675 m
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