Question

A stretched wire under a tension of 4 kg wt is in unison with a tuning fork of
frequency 512 Hz. How should the tension be altered to make the wire vibrate in
unison with a tuning fork of frequency 256 Hz?​

Answer 1

Answer:

Tension in the wire should be decreased to 1 kgwt

Explanation:

Frequency in a string of length "L", mass per unit density "μ" and under a tension "T" is given as

• f = 1/(2L) × √(T/μ)

In first case

f₁ = 1/(2L) × √(4g/μ)

512 = 1/(2L) × √(4g/μ)

In second case

f₂ = 1/(2L) × √(T'/μ)

256 = 1/(2L) × √(T'/μ)

Divide above two equations

512/256 = [1/(2L) × √(4g/μ)] / [1/(2L) × √(T'/μ)]

2 = √(4g/T')

4 = 4g/T'

T' = g

T' = 9.8 N

T' = 1 kgwt