A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe

(a) it is a closed pipe

(b) the fundamental frequency, is 88 Hz.

Explanation:

Given overtones;

The overtones for open pipes are given as;

The overtones for closed pipes are given as;

Where;

is the fundamental frequency

(a) From the given overtones;

test for open pipe;

396 Hz ≠ 440 Hz (it is not open pipe)

Test for closed pipe;

(b) the fundamental frequency, is 88 Hz.

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