Signals and systems — frequency from period A periodic pulse has a measured period of 15 ms. Calculate the signal's frequency in hertz (Hz), using f = 1 / T, and choose the closest value.

Introduction / Context:
In basic signals and systems, frequency and period describe the same repetitive behavior from two viewpoints. Frequency (in hertz) tells how many cycles occur each second, while period (in seconds) tells how long a single cycle lasts. Converting between them is a core skill used in electronics, communications, and instrumentation.

Given Data / Assumptions:

• Period T = 15 ms.
• We want frequency f in hertz (Hz).
• Use ideal relationship f = 1 / T with consistent SI units.

Concept / Approach:
The fundamental relationship for periodic signals is f = 1 / T. To apply it correctly, convert milliseconds to seconds because hertz uses per-second units. 1 ms = 10^-3 s, so 15 ms = 15 * 10^-3 s = 0.015 s.

Step-by-Step Solution:

Verification / Alternative check:
If T decreases, f increases proportionally. A 10 ms period corresponds to 100 Hz; since 15 ms is 1.5 times longer than 10 ms, the frequency should be 100 / 1.5 ≈ 66.7 Hz, confirming the result.

Why Other Options Are Wrong:

• 6.66 Hz: Off by a factor of 10 (used T in seconds but mistakenly scaled).
• 666.66 Hz: Off by a factor of 10 (likely used milliseconds without unit conversion).
• 15 Hz: Incorrectly treated period value as frequency directly.

Common Pitfalls:
Forgetting to convert milliseconds to seconds, mixing up period and frequency, or inverting the wrong value. Always check units before calculating.

Final Answer:
66.66 Hz