Standing waves are set up on two strings fixed at each end. The two strings have

Question

Standing waves are set up on two strings fixed at each end. The two strings have the same tension, but they differ in length by 0.57 cm. The waves on the shorter string propagate with a speed of 41.8 m/s, and the fundamental frequency of the shorter string is 225 Hz.

(a) Determine the fundamental frequency of the longer string.

(b) Determine the beat frequency produced by the two standing waves. Can you hear/discern this beat frequency?

(c) What is the shortest tube you could use to produce a standing wave in air of the same fundamental frequency as the shorter string (225 Hz)? Would it be an open-open (or closed-closed) tube or an open-closed tube? Assume that the speed of sound in air is 343 m/s.

Explanation / Answer

For shorter string

Length = L

V = speed = 41.8 m/s

f = frequency = 225Hz

f = V/2L

225 = 41.8 / 2L

L = 0.093 m

For longer string

L' = 0.093 + 0.0057 = 0.0987 m

f' = fundamental frequency = V/(2L')

f' = 41.8 / (2 x 0.0987) = 211.75 Hz

b)

beat frequency = 225 - 211.75 = 13.25 Hz

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