Ringing means the rise and decay time before and after the transducer reaches the maximum amplitude. Expressed as the mechanical Q of the transducer, which is the number of cycles it takes to get up to 90% of maximum amplitude or down to 10% above zero amplitude.

The dead or ring down zone is the distance from the front face of the transducer to the first echo that is identifiable. The signals from this region are unsuitable. The dead zone is the result of transducer ringing and reverberations from the interface between the transducer and the scanned object. Impedance matching between the transducer and the receiver is important to avoid electrical ringing.
With an increase of the frequency, the pulse length and the depth of the dead zone decrease, if all other parameters remain constant. The acoustic power also affects the depth of the dead zone.

Damping is a process, material, design, and mounting technique used to reduce the pulse duration or ringing of the transducer. Special material is applied to the back of the transducer in order to reduce the amplitude and pulse length of the sound wave.
Damping improves axial resolution by reducing pulse length. Thereby the lateral resolution increases.