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Question:

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be 32 cm, 40 cm, 28 cm, or 36 cm?

36 cm

32 cm

40 cm

28 cm

Solution:

Let the shortest resonating length be l1
And the next be l2
Then,
l1+e=λ/4 (1)
l2+e=3λ/4 (2)
Here, e = end correction
On dividing (1) by (2)
(l1+e)/(l2+e) = 1/3
(10+1)/(l2+1) = 1/3
11/(l2+1) = 1/3
33 = l2+1
l2 = 32 cm