The resonating air column in the open-closed pipe shown below is 0.635 m long. (

Question

The resonating air column in the open-closed pipe shown below is 0.635 m long.

(a) If the lowest frequency that can be produced by the pipe is 129 s-1, what is the temperature?

(b) The pipe is cut a distance d from the closed end (shown below by the dotted line) so that we now have two shorter pieces: an open-open piece and an open-closed piece. If the secondlowest frequency that can be produced by the open-open piece equals the third-lowest frequency that can be produced by the open-closed piece, what is d?

(c) Sketch the displacement amplitude variation for the second-lowest mode in the open-open piece and the pressure amplitude variation for the third-lowest mode in the open-closed piece.

Explanation / Answer

fo = V/4L

V = fo*4*L = 129*4*0.635 = 327.66 m/s

b)

2V/2*(L-d) = 5V/4d

1/(L-d) = 5/4d

4d = 5L - 5d

9d = 5L

d = 5L/9 = (5*0.635)/9

d = 0.3527 m

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