Q factor is _____ related to the pulse length.

• A. Directly
• B. Inversely
• C. Unrelated
• D. Exponentially

Answer: (A)

Q factor reflects how long energy stays stored in a resonant system versus how quickly it is lost. The pulse length you observe after excitation is directly tied to that energy decay: if the system loses energy slowly (high Q), the ring-down lasts longer, so the pulse is longer. The decay time is roughly proportional to Q divided by the center angular frequency, tau ≈ Q/ω0, which means increasing Q lengthens the time-domain response. Since a higher Q also means a narrower bandwidth, the time-domain signal tends to persist longer as well. So the pulse length is directly related to Q.

That’s why the direct relationship is the best choice. An inverse or exponential relation would imply the pulse shortens as Q grows, which isn’t correct, and being unrelated wouldn’t capture the tied physics of energy storage and decay.