A pipe is open at both ends. Its length is 22.81 cm. If I excite standing waves

Question

A pipe is open at both ends. Its length is 22.81 cm. If I excite standing waves in the pipe

by blowing air over one of its ends, I hear a pitch of 720.1 Hz. (a) Find the

distance between the antinodes at the two ends of the pipe. This is not the same as the

actual length of the pipe, since the antinodes are not exactly at the ends of the pipe. The

speed of sound is 343 m/s. (b) How far past the physical ends of the pipe do the

antinodes extend? Assume that it is the same amount for each antinode. (c) If I close

one end of the pipe, what pitch will I hear? The node at the closed end is exactly at the

position of the closed end. The antinode at the open end extends past the physical end of

the pipe by the same amount found in part (b).

Explanation / Answer

(a) open pipe: ?=2L , L=?/2
?= v/f= 345/726.1= 0.47514
L= ?/2= 0.23757m
(b) (0.23757-0.2281)/2= 0.00474= 4.7mm (end correction)
(c) f=v/?= v/4L= 345/4(0.2281+0.00474)= 370.433= 370.4[Hz] approx

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