Question

A wire of length 80 cm has a frequency of 256Hz . calculate the length of a similar wire under similiar tension which will have the frequency 1024Hz

Answer 1

we are talking about fundamental frequency of a standing wave on the wire fixed at both ends.

v = speed = √T/μ       ,μ = mass per unit length
                                   T = tension force
L = length of wire = λ/2

Frequency = v/λ =  v/2L = 1/2L * 1/√μ  * √T

L2 / L1  = f1 / f2
L2 = 80 * 256 / 1024 = 20 cm