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Deducing Mathematically

The end corre...

Question

The end correction of a resonance column is 1.0 cm. If the shortest length resonating with a tuning fork is 15.0 cm, the next resonating length is

A

31 cm

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B

45 cm

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C

46 cm

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D

47 cm

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Solution

The correct option is C 47 cm
Resonating length for open pipe is $3 l$ $= 3 (15) = 45 c m$
Since it is open at both ends, correction $= 2 c m$
$∴$ Length, $l^{'} = 45 + 2 = 47 c m$

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