Question

Calculate the first three overtones of a 1 m long boom-whacker that has a) both ends...

Calculate the first three overtones of a 1 m long boom-whacker that has a) both ends open and b) when one end is closed. Assume a room temperature of 25 degrees Celsius. (Ans: a) 3rd overtone: 670 Hz, b) 3rd overtone: 603.3 Hz.

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Homework Answers

Answer #1

The velocity of sound at 25 degrees, v = 347 m/s

a) Both ends open
Frequency of the fundamental tone, f1 = v/2L
Where L is the length of the boom-whacker.
f1 = 347/(2 x 1) = 173.5 Hz
First overtone, f2 = 2f1 = 2 x 173.5 = 347 Hz
Second overtone, f3 = 3f1 = 3 x 173.5 = 520.5 Hz
Third overtone, f4 = 4f1 = 4 x 173.58 = 694 Hz

b) One end closed
Frequency of the fundamental tone, f1 = v/4L
f1 = 347/(4 x 1) = 86.75 Hz
One end closed will produce only odd harmonics

First overtone, f2 = 3f1 = 2 x 86.75 = 260.25 Hz
Second overtone, f3 = 5f1 = 3 x 86.75 = 433.75 Hz
Third overtone, f4 = 7f1 = 4 x 86.75 = 607.25 Hz

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