Frequency bandwidth describes the range of frequencies within a pulse of ultrasound.
A wide range of frequencies is called a broad bandwidth, whereas a smaller range of frequencies is called a narrow bandwidth.
Historically, old single crystal transducers produced a pulse of sound that contained a limited range of frequencies. They, therefore, had a narrow bandwidth. Modern array transducers contain multiple small, highly damped crystal elements which allow them to transmit broad bandwidth pulses. This is why modern array transducers are often labeled in a format like this: L 12-3, or C 9 -5. In this example, an L 12-3 transducer is a linear array that has a bandwidth from 12 - 3 MHz. The C 9-5 transducer is a convex array transducer that has a bandwidth of 9 - 5 MHz.
Having this wide bandwidth provides these transducers with many advantages over the old single crystal transducers. We like broad bandwidths!
Quality factor (Q factor) is an engineering term that describes the "quality "of the sound. Q factor is inversely related to bandwidth. Broadband transducers produce low Q sound, whereas narrow bandwidth transducers produce high Q sound. In imaging, we like low Q sound. This may sound counterintuitive, so I have created a video below that explains these two concepts.