KinexiaLEARN PHYSICS

Standing Waves — Guitar Fundamental (Worked Example)

Easy
Problem

A guitar string 0.65 m long carries waves at 400 m/s. What is its fundamental frequency?

Given

  • L = 0.65 m

  • v = 400 m/s

  • n = 1

Find

The fundamental frequency f₁.

Principle

Fixed at both ends, the string fits half a wavelength: f_n = nv/(2L).

Formula

Solution

  1. Write the formula: f1=v/(2L)f_1 = v/(2L)

  2. Substitute: f1=400/(2×0.65)f_1 = 400/(2 \times 0.65)

  3. Denominator: 1.301.30

  4. Divide: f1=308 Hzf_1 = 308\ \mathrm{Hz}

308 Hz

Unit check

(m/s) ÷ m = Hz — correct.

What this means physically

308 Hz — near G4 on the musical scale. Pressing the fret shortens L and raises the pitch — the whole guitar is this formula made playable.

Common mistake

Using L instead of 2L. The fundamental fits half a wavelength on the string — the 2 is essential.