Question

Please help me with this calculation

__________________ <- A vibrating wire which is 4cm long

Diameter= 0.0002m
Frequency= 2500Hz
density of carbon steel= 7700kg/m3
How do i find the tension of this wire?

This is some of the equations which we should be using: v= √T/µ, v=fλ, f=(n/2l) *(√T/µ)

Answer 1

You need to derive the wave speed in the wire, v, from the mode picture and the frequency, f . Once you know the wave speed, use the equation
v= √(T/µ),
to get the tension, T.
µ is the mass per unit length, which you can get from the density and diameter.
µ = (pi d^2/4)*(density)

You also need the wavelength, λ, and that depends upon the number of nodes, n. I can't see wnhat n is from your straight line sketch.

Your equation f=(n/2l) is wrong. That is the equation for wavelength, λ .