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To determine the constant of proportionality, we can set up a proportion:
$\frac{\text{Amount of money earned}}{\text{Number of hours worked}} = \text{Constant of proportionality}$
We are given that Sarah earns $320 for working 40 hours. Plugging these values into the proportion:
$\frac{320}{40} = \text{Constant of proportionality}$
Simplifying the fraction:
$8 = \text{Constant of proportionality}$
Thus, the constant of proportionality is $\boxed{8}$.