At what depth is the phase of temperature profile reversed?

[rmjmu507]

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?

 

[Drakkith]

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.

 

[Baluncore]

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.