Question

A wire of length l having tension t and radius r with natural frequency f another wire of the same metal with length 2l having tension 2t and radius 2r will vibrate with natural frequency

Answer 1

Hey dear,

◆ Answer-
f' = f/2√2

◆ Explanation-
Fundamental frequency of waves on string is given by-
f = (1/2l) √(T/μ)
f = (1/2l)√(T/ρπr^2)

For another string,
f' = (1/4l) √(2T / 4ρπr^2)
f' = (1/2√2)(1/2l)√(T/ρπr^2)
f' = f/2√2

Therefore, f' = f/2√2.

Hope it helps...