Signal spectra: If a periodic waveform has a fundamental frequency of 400 Hz, what is the frequency of its fourth harmonic (i.e., the component at 4 * fundamental)?

Introduction:Harmonics are integer multiples of a waveform's fundamental frequency and are central to understanding spectra, distortion, and filtering. This question tests your ability to map an nth harmonic to its absolute frequency given the fundamental, a frequent task in signal analysis and power quality work.

Given Data / Assumptions:

• Fundamental frequency f1 = 400 Hz.
• We seek the fourth harmonic (n = 4).
• Ideal periodic signal with exact harmonic integer multiples.

Concept / Approach:By definition, the nth harmonic has frequency fn = n * f1. For n = 4, simply multiply the fundamental by 4. Converting between Hz and kHz (1 kHz = 1000 Hz) provides a convenient representation for larger values.

Step-by-Step Solution:

Verification / Alternative check:Check units: 400 Hz × 4 = 1600 Hz (not 4000 Hz). Cross-check that 1.6 kHz equals 1600 Hz, confirming consistency.

Why Other Options Are Wrong:

• 100 Hz: This is one-fourth of the fundamental, not the fourth harmonic.
• 4 kHz: Would be 10 * fundamental; incorrect multiple.
• 4 Hz: Far below the fundamental; not a harmonic.

Common Pitfalls:Confusing “4th harmonic” with “fundamental divided by 4”; mis-converting Hz to kHz; forgetting that harmonic numbers are integers greater than or equal to 1.

Final Answer:1.6 kHz