UPSEE Solved Model Paper 7

For resonance, the length of the air column is given by
L + ΔL = (2n+1)

λ

4

... (i)
where.
n = 0,1,2, 3,
ΔL end correction of the air column
It is given that the length of the air column that resonates in the fundamental mode with a tuning fork is 0.2 m
For fundamental mode, n = 0
Using eq (I),
0.2 m + ΔL =

λ

4

... (ii)
When the length of the resonating column changes to 0.70 m, it resonates in the first overtone.
This happens when n = 1. Eq (i) gives
0.70 m + ΔL =

3λ

4

... (iii)
Substituting the value of eq (ii) in eq (iii), we get
0.70 m + Δ L = 3 (0 .2 m + ΔL)
⇒ 0.70 m - 0.60 m = 3 Δ L - Δ L
⇒ 0.10 m = 2 Δ L
⇒ ΔL = 0.05 m
This represents the end correction of the air column
Hence: option 'D' is correct