In class, we have seen the first three harmonics in an \"open tube\'\' (which me

Question

In class, we have seen the first three harmonics in an "open tube'' (which means a tube open on BOTH ends, like e.g. a flute). You can find this situation described in the course textbook as well. The pressure pattern is just like that of the normal modes of a string.
If a flute is fingered so it has a length of 0.40 m, what will be the frequency of the fundamental note you hear? (Assume the air is at room temperature.)

In class, we have also seen the first three harmonics in a "closed tube'' (which means a tube open on ONE end, but sealed off on the other, like e.g. a clarinet). You can find this situation described in the course textbook as well.
If a clarinet is fingered so it has a length exactly the same as the flute in the first part of the question question (i.e. 0.40 m) what's the frequency of the fundamental note you hear? (Assume the air is at room temperature.)

Explanation / Answer

1) For pipe opened at both ends,

fundamental frequency = v/2L = 343/(2*0.40)

= 428.75 Hz

2) for pipe closed at one end,

Fundamental frequency = v/4L = 343/(4*0.40)

= 214.375 Hz

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