  We study the frequency and angular dependences of Cherenkov radio pulses
originated by the excess of electrons in electromagnetic showers in different
dense media. We develop a simple model to relate the main characteristics of
the electric field spectrum to the properties of the shower such as
longitudinal and lateral development. This model allows us to establish the
scaling of the electric field spectrum with the properties of the medium such
as density, radiation length, Moliere radius, critical energy and refraction
index. We normalize the predictions of the scaling relations to the numerical
results obtained in our own developed GEANT4-based Monte Carlo simulation, and
we give a unified parameterization of the frequency spectrum and angular
distribution of the electric field in ice, salt, and the lunar regolith, in
terms of the relevant properties of the media. Our parameterizations are valid
for electromagnetic showers below the energy at which the
Landau-Pomeranchuk-Migdal effect starts to be relevant in these media. They
also provide an approximate estimate of radio emission in hadronic showers
induced by high energy cosmic rays or neutrinos.
