A cylindrical tube, open at both ends, has a fundamental frequency v. The tube is dipped vertically in water so that ,

Monjur Alahi

A cylindrical tube, open at both ends, has a fundamental frequency v. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is

(a) v/4

(b) v/2

(c) v

(d) 2v.


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Salim Ahmed Kawsar

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The correct answer is (c) v

EXPLANATION: 

When a tube of length L open at both ends has a fundamental frequency ν, then v = V/2L where V is the velocity of the sound wave. When this tube is half dipped in water, the length of the air column becomes L/2 and it becomes a tube closed at one end. In such closed pipe the frequency of the fundamental mode ν' = V/4L'. Here L' = L/2, so ν' = V/(4*L/2) = V/2L = ν 

Hence the option (c).

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