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An air column, closed at one end and open at the other, resonates with a tunning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tunning fork is
A
100 cm
B
150 cm
C
200 cm
D
66.7 cm
Explanation
Resonance lengths are λ/4, 3λ/4, ...
Detailed Solution
For a closed pipe, the first resonating length $l = \frac{\lambda}{4} \Rightarrow \lambda = 4l$ ...(i)
Next resonating length $l' = \frac{3\lambda}{4} = \frac{3\times4l}{4} = 3l$
$l' = 3\times50$ cm = 150 cm
Next resonating length $l' = \frac{3\lambda}{4} = \frac{3\times4l}{4} = 3l$
$l' = 3\times50$ cm = 150 cm