If a sine wave has a frequency of 500 Hz, what is its period in seconds? (Recall: period T = 1 / f.)

Introduction / Context:
Frequency and period are reciprocals for a periodic signal. This fundamental relationship appears in physics, electronics, and signal processing. Being able to convert between frequency in hertz and period in seconds is essential for timing design, sampling selection, and filter specification.

Given Data / Assumptions:

• Frequency f = 500 Hz.
• Definition: T (seconds) = 1 / f (hertz).
• We assume an ideal sinusoid with constant frequency.

Concept / Approach:
Use the basic formula T = 1 / f. Substitute the given frequency and compute the reciprocal. Ensure units: if f is in Hz (cycles per second), T will be in seconds per cycle.

Step-by-Step Solution:

Verification / Alternative check:
Convert to milliseconds: 0.002 s = 2 ms, which is reasonable for a 500 Hz signal (500 cycles per second means 2 ms per cycle).

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting units; confusing milliseconds and seconds; inverting the relationship incorrectly.

Final Answer:
0.002