If a communication system performs effectively in between 200 Hz to 3.4 kHz, what is its bandwidth?
3.2 kHz
Bandwidth is the width of the band of frequencies a system can effectively pass, calculated as the difference between the highest and lowest usable frequency:
Bandwidth = Upper cut-off frequency − Lower cut-off frequency
Here the system operates effectively from a lower frequency of 200 Hz to an upper frequency of 3.4 kHz. Converting to a common unit (3.4 kHz = 3400 Hz):
- Bandwidth = 3400 Hz − 200 Hz = 3200 Hz = 3.2 kHz.
This value is close to the classic telephone voice channel (roughly 300 Hz to 3400 Hz), which is why speech transmission systems are commonly quoted as having a bandwidth of about 3.1–3.4 kHz. Bandwidth matters because it fixes how much frequency content — and therefore how much information — the channel can carry.
Common wrong answers arise from mishandling the two numbers: 3.4 kHz is simply the upper frequency, not the difference; 200 Hz is only the lower frequency; and 3.6 kHz comes from mistakenly adding 200 Hz to 3.4 kHz instead of subtracting. Bandwidth is always a subtraction of the two band edges, giving 3.2 kHz.
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