Which statement correctly describes the relationship between event duration and bandwidth?

Which statement correctly describes the relationship between event duration and bandwidth?

• A. Long duration events are wide bandwidth
• B. Long duration events are narrow bandwidth
• C. Short duration events are narrow bandwidth
• D. Short duration events are wide bandwidth

Answer: (B)

The relationship being tested is that how long something lasts and how wide its frequency content is are inversely related. When an event extends over a long period, its frequency content is concentrated in a smaller range, giving it a narrow bandwidth. Conversely, a short, rapid event requires many different frequencies to reproduce the sharp changes, so it has a wide bandwidth. A simple way to see this is that the spectrum of a pulse of duration T broadens roughly as 1/T: longer duration means smaller spectral spread, shorter duration means larger spectral spread. So a long-lasting event sits in a narrow frequency range, while a short, quick event spreads across a wide range of frequencies. That’s why the statement that long duration events are narrow bandwidth is the correct description.

The relationship being tested is that how long something lasts and how wide its frequency content is are inversely related. When an event extends over a long period, its frequency content is concentrated in a smaller range, giving it a narrow bandwidth. Conversely, a short, rapid event requires many different frequencies to reproduce the sharp changes, so it has a wide bandwidth. A simple way to see this is that the spectrum of a pulse of duration T broadens roughly as 1/T: longer duration means smaller spectral spread, shorter duration means larger spectral spread. So a long-lasting event sits in a narrow frequency range, while a short, quick event spreads across a wide range of frequencies. That’s why the statement that long duration events are narrow bandwidth is the correct description.