gen-define-resonance-and-harmonics-and-give-one-short-worked-exa-8b67

Define resonance and harmonics and give one short worked example.

# Resonance and Harmonics ## **Resonance** Resonance occurs when a system is driven at its natural frequency of vibration, causing a dramatic increase in amplitude. Every object has natural frequencies at which it "prefers" to vibrate. ## **Harmonics** Harmonics are integer multiples of a fundamental frequency. For a vibrating string or air column: - **1st harmonic (fundamental)**: f₁ = lowest frequency - **2nd harmonic**: f₂ = 2f₁ - **3rd harmonic**: f₃ = 3f₁, etc. --- ## **Worked Example: Guitar String** **Given:** A guitar string is 0.65 m long and vibrates at a fundamental frequency of 330 Hz. **Find:** The frequencies of the 2nd and 3rd harmonics. **Solution:** For a string fixed at both ends: - **Fundamental (1st harmonic)**: f₁ = 330 Hz - **2nd harmonic**: - f₂ = 2f₁ = 2(330) = **660 Hz** - **3rd harmonic**: - f₃ = 3f₁ = 3(330) = **990 Hz** **Physical meaning:** The string can vibrate in 1, 2, or 3 segments. When you pluck it, you typically excite multiple harmonics simultaneously, which gives the guitar its characteristic rich sound.