gen-define-the-fundamental-frequency-and-give-one-short-worked-e-b27a

Define the fundamental frequency and give one short worked example.

# Fundamental Frequency **Definition:** The fundamental frequency is the **lowest natural frequency** at which a system vibrates or resonates. It corresponds to the first harmonic or primary mode of oscillation. For physical systems: - **Strings/columns:** It's the frequency when the system vibrates in its simplest pattern (fewest nodes) - **General:** f₀ = 1/T₀, where T₀ is the period of one complete oscillation --- ## Worked Example **Problem:** Find the fundamental frequency of a guitar string that is 65 cm long, where waves travel at 400 m/s. **Solution:** For a string fixed at both ends, the fundamental frequency occurs when the length equals half a wavelength: L = λ/2 65 cm = λ/2 λ = 2 × 0.65 m = 1.3 m Using the wave equation: $$f_0 = \frac{v}{\lambda} = \frac{400 \text{ m/s}}{1.3 \text{ m}} = 308 \text{ Hz}$$ **Answer:** The fundamental frequency is **308 Hz** (approximately E₄ on the musical scale).