Q.A sinusoidal message signal of frequency 10 kHz amplitude-modulates a carrier wave. Calculate the bandwidth required to transmit this amplitude-modulated signal.

Bandwidth is the width of the frequency band needed to faithfully carry a signal (or that a device can handle), i.e. $f_{max}-f_{min}$.

Any practical signal (e.g. speech, music, video) is not a single pure frequency but a superposition of many frequency components spread over a range. The bandwidth of that signal is the difference between the highest and lowest significant frequencies it contains:

$\text{Bandwidth} = f_{max}-f_{min}$ …

This tests standard bandwidth values quoted for common signals in communication systems (a chapter not in the current syllabus, answered here for completeness).

Typical bandwidth requirements quoted for common signals:

• T.V. signal bandwidth ≈ 6 MHz (video + audio + guard bands, as used for a TV channel) → (c) 6 MHz
• Speech signal bandwidth ≈ 2800 Hz (telephone-quality speech, roughly 300 Hz–3100 Hz) → (d) 2,800 Hz …

Because optical carrier waves have extremely high frequencies (order 10^14 Hz), even a small fractional bandwidth translates into an enormous absolute bandwidth for optical fibre communication — of the order of 100 GHz, far exceeding radio/microwave systems.

The information-carrying capacity (bandwidth) of a communication channel scales with the frequency of the carrier wave used — roughly, a usable bandwidth is some fraction of the carrier frequency. Radio waves and microwaves used in conventional communication have carrier frequencies of order 10^6-10^10 Hz, limiting their bandwidth accordingly.

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