At what depth is the phase of temperature profile reversed?

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rmjmu507
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The amplitude of daily temperature is dT=5 C. The ground is made of limestone.

At what depth is the phase of temperature profile reversed (cooler at 3 pm and warmer at 3 am)?

Circular frequency is equal to I think 2E-7 per second

The depth at which the profile is reversed is where the cosine function switches signs, i.e. at pi.

So, I find that the profile is reversed at 7.9 meters. Does this seem correct?

How could I find the ratio of the amplitude of temperature variation at 7.9 m vs. the temperature variation at the surface?
 
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Replying so that this thread isn't a no-reply, as per Greg's wishes.
If anyone sees this and has knowledge on the subject, feel free to respond.
 
rmjmu507 said:
Circular frequency is equal to I think 2E-7 per second
I would question that.
Period T = 24 hours = 24 * 60 * 60 = 86400 sec .
Frequency in Hz = 1 / T ;
Angular freq = 2 * Pi / 86400 = 72.722x10-6 rad/sec.

This problem is a one dimensional thermal diffusion equation.
The depth will depend on the thermal conductivity of the limestone.