Signal basics: A periodic signal has a period of 400 µs (microseconds). What is its frequency in hertz (Hz)?
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A2,500 Hz
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B250 Hz
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C25,000 Hz
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D400 Hz
Answer
Correct Answer: 2,500 Hz
Explanation
Introduction / Context:Frequency–period relationships are foundational in electrical engineering and signal processing. Knowing either the period (time for one cycle) or the frequency (cycles per second) allows you to compute the other. This question tests conversion from a given period in microseconds to frequency in hertz.
Given Data / Assumptions:
- Period T = 400 µs.
- 1 µs = 10^-6 s.
- Ideal, perfectly periodic waveform (no jitter).
Concept / Approach:
The period T and frequency f are reciprocals: f = 1 / T. Convert microseconds to seconds first to avoid scale errors, then take the reciprocal to obtain frequency in hertz.
Step-by-Step Solution:
Convert period: T = 400 µs = 400 * 10^-6 s = 4.00 * 10^-4 s.Apply reciprocal relation: f = 1 / T.Compute: f = 1 / (4.00 * 10^-4) = 2.5 * 10^3 Hz = 2,500 Hz.Verification / Alternative check:
A period of 1 ms corresponds to 1,000 Hz. Since 400 µs is less than 1 ms, the frequency should be greater than 1,000 Hz. 2,500 Hz fits this expectation.
Why Other Options Are Wrong:
250 Hz corresponds to T = 4 ms. 25,000 Hz corresponds to T = 40 µs. 400 Hz corresponds to T = 2.5 ms. None match 400 µs.
Common Pitfalls:
Forgetting to convert µs to s; placing the decimal incorrectly when taking reciprocals; confusing kHz and Hz.
Final Answer:
2,500 Hz