If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?
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This is Giancoli Answers with Mr. Dychko.. Organ pipes that are open on both end will have harmonics equal to n times the fundamental, where n is a natural number 1, 2, 3, 4 or 5. And so the fundamental of the lowest frequency sound at the bottom range of the human hearing, 20 hertz. The fundamental will be v divided by 2 times the length that we're gonna have to figure out, length at 20 hertz. And this is the formula for fundamental for an a tube open at both ends. And we multiply both sides by l, 20 hertz, divided by the fundamental, and we get this formula here it's v over 2 times the fundamental. So, that's 343 meters per second divided by 2 times 20 hertz which is about 8.6 meters in length. Now, the fundamental for the top of the range of human hearing is going to, the fundamental frequency will be 20 times 10 to the 3 hertz, 20 kilohertz. And the length in that case will be 343 meters per second divided by 2 times 20 times 10 to 3 hertz which is about 8.6 millimeters which is very short
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