Final answer:
The half frequencies for a system where Q >> 1 are given by signal processing equations. These frequencies are related to the quality factor, Q, of the system, indicating the sharpness of resonance.
Step-by-step explanation:
If Q >> 1, then the half frequencies, often referred to as the upper and lower half-power frequencies (fu, fl), are given by signal processing equations. This relates to the quality factor, Q, which describes the sharpness of the resonance of a system. A system with a high Q factor will have a narrow bandwidth around its resonant frequency, and the two half-power frequencies are close to each other, defining a sharp peak in the frequency response. In the context of electrical engineering and acoustics, the Q factor is particularly relevant when designing filters and resonators.
The relationship Q is proportional to B suggests the interplay between the spread in the frequencies at half the amplitude and the natural frequency, depicted by the quality of a system. The Q factor is used to determine the quality of resonance in terms of energy loss versus energy stored within the system.