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Question

Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340ms1.


A

120, 240 360 Hz

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B

850 Hz, 1750 Hz, 2550 Hz

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C

150, 300 450 Hz

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D

None of these

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Solution

The correct option is B

850 Hz, 1750 Hz, 2550 Hz


Fundamental frequency First overtone

λ2 = L 2(λ2) = L

λ = 2L f = vL

λ f = v vf = 2L

f = v2L

If V = 340ms,L = 20 cm = 20 × 102m

Fundamental frequency =V2L = 3402 × 20 × 102 = 850 Hz

we know first overstone =2V2L = 2 × 3402 × 20 × 102 (for open pipe) = 1750 Hz

Second overtone =3(V2L) = 3 × 850 = 2550


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