If 27MHz radio waves penetrate to a depth of 14cm , estimate the depth of penetration of 3.0GHz microwaves.

For radio and microwaves, the depth of penetration into the human body is approximately proportional to the square-root of lambda

We know that c = lambda * freq and that p = factor * sqrt(lambda)

c = is the speed of light
p is for penetration, p_k for known penetration, p_u for unknown penetration

p_k / p_u = factor * sqrt (lambda_k) / factor * sqrt(lambda_u) = sqrt (lambda_k) / sqrt(lambda_u)

( p_k / sqrt (lambda_k) ) * sqrt (lambda_u) = p_u = 1.48 m or it goes through the entire body.