In a experiment to determine velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz. Velocity of sound at room temperature is 336 m/s. The third resonance is observed when air column is at length of _____ (in cm)

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100 cm

104 cm

80 cm

84 cm

answer is C.

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Detailed Solution

$λ = \frac{V}{f} = \frac{336}{400} = 84 c m$

At first resonance, $\frac{λ}{4} = l + e \Rightarrow e = 1 c m$
At 3^rd resonance, $l_{3} + e = \frac{5 λ}{4}$ .

$\Rightarrow l_{3} = 5 (21) - 1 = 104 c m$

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