To find out the frequency of AC mains using a sonometer

[Samar99]

Homework Statement

There is this experiment regarding the frequency of AC mains using a sonometer and I found a slight confusion with the formula. there is an electromagnet attached to a step down transformer and a wire is placed below the electromagnet, and by varying the length and tension, one has to get the maximum amplitude deflection,so as to match the natural frequency of the wire with the electromagnet.

Homework Equations

the frequency of oscillation of a wire is given by
f=1/2L√T/μ
where, L= length of wire
T=Tension in the string
μ=Mass per unit length

The Attempt at a Solution

the formula gives the frequency of the wire, not the AC mains. Here in India, AC mains frequency is 50 Hz, so the electromagnet gets magnetized and demagnetized twice in a cycle so the wire should be pulled towards the electromagnet 100 times. So should I halve the frequency that I get from the above formula to get the frequency of AC mains?

 

[technician]

Everything is OK
When the current flows in one direction the wire experiences an upward force and when the current reverses the force reverses. So the frequency of the wire is the frequency of the AC.
When the amplitude is maximum the wire is resonating at the mains frequency.
The first occasion resonance occurs is when the wire is half a wavelength long.
This is the reason for the 1/2L in the equation