Question

A stretched uniform wire of length L under tension T is vibrating with frequency 'n' . A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is increased by 16 N, it is in resonance with 2^nd harmonic of same closed pipe. The initial tension in the wire is ______.

विकल्प

• 2 N

• 1 N

• 1.5 N

• 0.5 N

Answer 1

A stretched uniform wire of length L under tension T is vibrating with frequency 'n' . A closed pipe of same length is also vibrating with same fundamental frequency 'n'. If T is increased by 16 N, it is in resonance with 2^nd harmonic of same closed pipe. The initial tension in the wire is 2 N.

Explanation:

n = `1/(2l) sqrt("T"/"m") = "v"/(4l)`

`= 1/(2l) sqrt(("T + 16")/"n") = (3"v")/(4l)`

`sqrt("T"/("T + 16")) = 1/3`

`"T"/("T + 16") = 1/9`

9T = T + 16

∴ 8T = 16

∴ T = 2 N