A piccolo is essentially a 32.0-cm long tube that is open at both ends. (a) What

Question

A piccolo is essentially a 32.0-cm long tube that is open at both ends.

(a) What are the frequencies of the fundamental (lowest note the instrument can play) and the next two harmonics of the piccolo? Assume v = 343 m/s for air.

f1 = ______________

f2 = ______________

f3 = ______________

(b) To tune a piccolo, the player changes the overall length of the instrument by either pushing together or pulling apart on two segments of the tube at one of the joints. Suppose a player tunes a piccolo in this way so that its total length is now 32.7 cm. What is the fundamental frequency now?

(c) Now suppose the piccolo from part (b) plays this fundamental frequency at the same time as another, 32.0-cm-long piccolo plays its own fundamental frequency. What beat frequency will be heard when this happens?

Explanation / Answer

a) f1 = V/2L = 343/(2*0.32) = 535.93 Hz

f2 = 2 f1 = 2V/2L = 343/(2*0.32) =1071.86 Hz

f3 = 3f1 = 3V/2L = 343/(2*0.32) = 1607.79 Hz

b) fo = V/2L1 = (343)/(2*0.327) = 524.46483 Hz

c) beats = f1 - fo = 11 Hz

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