To get a lower bound for the bass note of 
,
we will apply a classical method from physics called
Rayleigh's cutting method.
This method was introduced by Rayleigh
[14]
as a way of estimating
the bass note of a Helmholtz resonator.
The idea is to cut the system into
pieces whose lowest eigenvalue can be estimated,
and then observe that if the lowest eigenvalue of each of the pieces
is 
,
then the lowest eigenvalue of the original system is .