A resonance tube of circular cross-section is used with a 500 Hz tuning fork. The speed of sound is 340 m/s and the first resonance occurs when the measured air-column length is 16.4 cm. Using the approximation e = 0.6r, where r is the tube radius, what is the tube radius?
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Question

A resonance tube of circular cross-section is used with a 500 Hz tuning fork. The speed of sound is 340 m/s and the first resonance occurs when the measured air-column length is 16.4 cm. Using the approximation e = 0.6r, where r is the tube radius, what is the tube radius?

Options

G1 Physics · Accepted Answer

For first resonance, l+e = λ/4 = v/(4f). Therefore, l+e = 340/[4(500)] = 0.17 m = 17.0 cm. Given measured length, l = 16.4 cm. Thus, e = 17.0−16.4 = 0.6 cm. Using e = 0.6r, 0.6 = 0.6r. Therefore, r = 1.0 cm. Correct option: B.