Argument for relationship between scale length and frequency

[Eric_meyers]

Homework Statement

Give an argument for there being a connection between scale length and frequency

Homework Equations

scale length = (wave length) / (Length)

The Attempt at a Solution

So from only my physical intuition I'm coming up with the longer the scale length the longer the wave length and thus by f = v/(lambda) the smaller the frequency. But is there a more physical interpretation of this?

 

[Zaphys]

It comes from the wave eq. (in one dimension, for instance):

$$\partial$$²y/$$\partial$$x²=1/v²·$$\partial$$²y/$$\partial$$t²

as v is derivated from the tension on the string and its linear density.