Question

A column of air of length 50cm resonates with a stretched string of length 40cm. The length of the same air column which will resonate with 60cm of the same string at the same tension is……….

(A) 100cm 

(B) 75cm 

(C) 50cm 

(D) 25cm

Answer 1

The correct option (B) 75 cm   

Explanation:

given: air column of length 50cm resonates with string of length 40cm.

For string of 60 cm, length of resonating air column is asked.

∴ ℓ₁  = 40cm

ℓ₁'  = 50cm

ℓ₂   = 60cm

 ℓ'₂  = ?

As (ℓ₂/ℓ₁) = (ℓ₂'/ℓ₁')

∴ (60/40) = (ℓ₂'/50)

∴ ℓ₂' = 75 cm