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Question
A glass tube is open at both ends. A tuning fork of frequency f resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now that air column inside the tube is in unison with another fork of frequency f, ____________.
Options
f' = f
f' = 4f
f' = 2f
f' = `"f"/2`
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Solution
A glass tube is open at both ends. A tuning fork of frequency f resonates with the air column inside the tube. Now the tube is placed vertically inside water so that half the length of the tube is filled with water. Now that air column inside the tube is in unison with another fork of frequency f, f' = f.
Explanation:
`l = lambda/2 Rightarrow lambda = 2l`
`therefore "f"="v"/lambda = "v"/(2l)` .....(i)
In second case,
`l/2 = (lambda')/4`
`therefore lambda' = 2l`
`"f"' = v/(lambda') = v/(2l)` .....(ii)
From (i) and (ii),
f' = f
