Question

what is define bandwidth in terms of Q

Answer 1

The bandwidth {\displaystyle \Delta f=f_{2}-f_{1}} of a damped oscillator is shown on a graph of energy versus frequency. The Qfactor of the damped oscillator, or filter, is {\displaystyle {\frac {f_{c}}{\Delta f}}}. The higher the Q, the narrower and ‘sharper’ the peak is.

In physics and engineering the quality factoror Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is,[1] and characterizes a resonator's bandwidth relative to its centre frequency.[2]Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping, so that they ring or vibrate longer