The period of a signal is 100 ms. Its frequency is _________.
2018
The period of a signal is 100 ms. Its frequency is _________.
Answer: B. 10⁻² kHz — Concept: Frequency and period are reciprocals of each other for a periodic signal: f = 1/T, where T is the period (time for one complete cycle) in seconds and…
- A.
10³ Hertz
- B.
10⁻² kHz
- C.
10⁻³ kHz
- D.
10⁵ Hertz
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Correct answer: B
Concept: Frequency and period are reciprocals of each other for a periodic signal: f = 1/T, where T is the period (time for one complete cycle) in seconds and f is the frequency in hertz (Hz). A shorter period corresponds to a higher frequency, and vice versa.
Application:
Convert the given period to seconds: T = 100 ms = 100 × 10⁻³ s = 0.1 s.
Apply the formula f = 1/T: f = 1/0.1 s = 10 Hz.
Convert the frequency to kilohertz, since 1 kHz = 1000 Hz: f = 10/1000 kHz = 0.01 kHz = 10⁻² kHz.
Cross-check: Reversing the conversion confirms the result — 10⁻² kHz = 0.01 kHz = 0.01 × 1000 Hz = 10 Hz, and the corresponding period is T = 1/f = 1/10 Hz = 0.1 s = 100 ms, which matches the period stated in the question.
Final answer: 10⁻² kHz, equivalently 10 Hz.