How Does Tension Affect Guitar String Frequency Beyond Basic Equations?

[IsaacsA]

Hi all!
I am currently conducting an investigation into the way in which frequency varies when you change the tension on a guitar string.
I am aware of Mersenne's laws, and that frequency should vary in square root proportion to tension. I'm looking for an explanation that goes beyond simply the formulae regarding the relationship, perhaps on a more microscopic scale.
In any case, I've searched a number of resources and I haven't been able to discern any reasonable explanation beyond the equation that exists.
Does anyone know of why frequency varies in square root proportion to tension, beyond simply the equation?

Mersenne's equation no. 22:

f(1)=v/λ=[1/(2L)](T/μ)^1/2

 

[AlephZero]

What do you already know about vibrations?

The equation is easy to derive from Newton's laws of motion (Google will find lots of references ), once you know calculus and partial differential equations, but I guess from the question that you don't know that much math.

Do you know about simple harmonic motion, and the vibration of a mass on a spring?