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Grade 11Wave Motion

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.

Profile image of Simran Bhatia
12 Years agoGrade 11
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1 Answer

Profile image of Aditi Chauhan
12 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