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?