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A tube of a certain diameter and of length 48 cm is open at both ends. Its fundamental frequency of resonance is found to be 320 Hz. The velocity of sound in air is 320 m/sec. Estimate the diameter of the tube.

A tube of a certain diameter and of length 48 cm is open at both ends. Its fundamental frequency of resonance is found to be 320 Hz. The velocity of sound in air is 320 m/sec. Estimate the diameter of the tube.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Hello Student,
Please find the answer to your question
Tube open at both ends:
(a) v = v/2(ℓ + 0.6 D) ∴ 320 = 320/2(0.48 + 0.6 x D)
0.48 + 0.6 D = 0.5 ⇒ 0.6 D = 0.02
⇒ D = 0.02/60 x 100 cm = 3.33 cm
Tube closed atone end:
V = v/4(ℓ + 0.3 D) = 320/4 (0.48 + 0.3 x 0.033)
= 163 Hz

Thanks
Aditi Chauhan
askIITians Faculty

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