- #1
bobred
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Homework Statement
Determine at what depth below the surface the temperature never falls
below zero.
Homework Equations
[tex]\theta(x)=\bar{\theta}+\theta_0\cos\left(\omega t-\sqrt{\dfrac{\omega}{2D}}x\right)\exp\left(-\sqrt{\dfrac{\omega}{2D}}x\right)[/tex]
where the average is [itex]\bar{\theta}=2.5[/itex] and amplitude [itex]\theta_0=7.5[/itex]
The Attempt at a Solution
At a depth x the temperature will be reduced by a factor
[tex]\exp\left(-\sqrt{\dfrac{\omega}{2D}}x\right)[/tex]
so for some ratio R
[tex]R=\exp\left(-\sqrt{\dfrac{\omega}{2D}}x_{min}\right)[/tex]
I'm having trouble figuring out what R is so that I can find [itex]x_{min}[/itex].
Any suggestions?