A sine wave has a period T = 0.001 second. In basic signal processing terms, what is its frequency f in hertz (Hz)?

Introduction / Context:
Frequency and period are reciprocal quantities for periodic signals. The frequency tells us how many cycles occur per second, while the period tells us how long each cycle lasts. Converting between them is a common task in electronics, communications, audio, and control engineering, as well as in computer timing and sampling problems.

Given Data / Assumptions:

• Period T = 0.001 second (that is, one millisecond per cycle).
• We assume a stable, perfectly periodic sine wave.
• We need frequency in hertz (cycles per second).

Concept / Approach:
The relationship is f = 1 / T. When T is in seconds, f is in hertz (Hz). Always check units carefully to avoid order-of-magnitude mistakes. For millisecond-scale periods, frequencies will typically be in kilohertz (kHz).

Step-by-Step Solution:

Verification / Alternative check:
Convert units first: T = 1 ms = 10^-3 s; therefore f = 1 / (10^-3) = 10^3 = 1000 Hz. This alternative unit-based reasoning confirms the arithmetic.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing milliseconds with microseconds, and forgetting to include units, can cause 10x or 1000x errors. Always write f = 1 / T with T in seconds to avoid mistakes.

Final Answer:
1,000 Hz.