Square wave harmonics: A square wave has a period of 60 µs. What is the frequency of the first odd harmonic beyond the fundamental?

Introduction / Context:Square waves contain only odd harmonics (1st, 3rd, 5th, … multiples of the fundamental frequency). The 'first odd harmonic' beyond the fundamental is the 3rd harmonic. Recognizing this is essential in spectra, filtering, and pulse-shaping design.

Given Data / Assumptions:

• Period T = 60 µs → fundamental f1 = 1/T.
• Square wave with standard Fourier content (odd harmonics only).

Concept / Approach:Compute f1, then multiply by 3 to obtain the 3rd harmonic. Convert microseconds to seconds carefully to avoid order-of-magnitude mistakes.

Step-by-Step Solution:

Verification / Alternative check:Quick check: If T = 60 µs, then 1/T = 16.67 kHz; triple is exactly 50.0 kHz. This aligns with the classic harmonic structure of square waves.

Why Other Options Are Wrong:

• 33.33 kHz: That would be 2 * 16.67 kHz (an even harmonic, which is absent).
• 500 kHz or 5 kHz: Not related to 3 × 16.67 kHz; they are an order of magnitude off.

Common Pitfalls:

• Assuming the 'first harmonic' means the fundamental itself; here it explicitly asks for the first odd harmonic beyond the fundamental (the 3rd).

Final Answer:50 kHz