Clock timing calculation: What is the period of a clock waveform with frequency f = 15.4 kHz? (Give the closest option.)

Introduction / Context:
Converting between frequency and period is a bread-and-butter skill in digital and analog electronics. Timers, baud rates, PWM, and sampling all rely on the relationship T = 1 / f.

Given Data / Assumptions:

• Frequency f = 15.4 kHz.
• We want the period T in microseconds.
• Use exact reciprocal without rounding errors that change the order of magnitude.

Concept / Approach:
The fundamental relationship is T = 1 / f. Convert units carefully: 1 kHz = 10^3 Hz; 1 µs = 10^-6 s.

Step-by-Step Solution:
Convert frequency to Hz: f = 15.4 kHz = 15,400 Hz.Compute period: T = 1 / 15,400 s ≈ 0.000064935 s.Convert seconds to microseconds: 0.000064935 s * 10^6 µs/s ≈ 64.935 µs.Closest option listed: 64.9 µs.

Verification / Alternative check:
Check with rough mental math: 1/10 kHz = 100 µs; 1/20 kHz = 50 µs; 15.4 kHz should be between them, near 65 µs. This aligns with 64.9 µs.

Why Other Options Are Wrong:
649 µs: Off by a factor of 10.6.49 µs and 0.649 µs: Off by factors of 10 and 100 respectively (too fast).6.49 ms: Off by 100× in the other direction (too slow).

Common Pitfalls:
Missing unit conversions (kHz vs. Hz, s vs. µs) and misplacing decimal points in reciprocals.

Final Answer:
64.9 µs