How far from the mouthpiece of the flute in Example 12–11 should the hole be that must be uncovered to play F above middle C at 349 Hz?
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This is Giancoli Answers with Mr. Dychko. We can model the flute as an open tube at both ends where one open end is the mouthpiece where you're blowing air across and the other open end is the hole, the fingering hole that has to be opened. So, the first fingering hole that has to be opened is this distance where you create half of the fundamental wavelength. And so the fundamental frequency is going to be the wave speed which is the speed of sound since the thing that's resonating here is the air inside the flute, divided by 2 times the length. And this is the length here, distance between the mouthpiece and the finger hole. And we can solve for the length by multiplying both sides by l over f1. And on the left side f1's cancel, leaving us with l equals v over 2 f1. So, that's 343 meters per second divided by 2 times 349 hertz which is about 50 centimeters or 0.491 meters.
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