Propagation of broadband ultrasound in attenuating media

An expression describing the time dependent evolution of broadband ultrasound wave forms is derived for signals propagating in a homogeneous tissue equivalent medium with an attenuation coefficient which is linearly proportional to frequency and for a class of pulse modulations which are analytic in the complex frequency plane. Results of the analysis are compared with those obtained by using a simple Gaussian modulation. It is shown that the frequency down shift produced by the medium causes predictable modifications in ultrasound beam widths and theoretical estimates are compared with published experimental data.