We present a methodology to obtain frequency-dependent relative site amplification factors using ambient seismic noise. We treat a seismic network or array as a forced damped harmonic oscillator system where each station responds to a forcing function obtained from frequency-wavenumber beams of the ambient noise field. A network or array beam is necessary to estimate the forcing function. Taken over long time periods, each station responds to the forcing function showing a frequency-dependent resonance peak whose amplitude and spectral width depends upon the elastic and anelastic properties of the underlying medium. Our results are encouraging in that hard rock sites show little variability and have narrower resonance peaks with reduced amplitudes relative to soft rock sites in sedimentary basins. There is much more variability observed at soft rock sites and a tendency for spectral peaks to shift to higher frequencies and become broader as the site amplification increases. This could be due to due to lower densities and/or small-strain nonlinearity at stations having high site amplification.