KinexiaLEARN PHYSICS

Wave Speed — Vibration on a Guitar String (Worked Example)

Easy
Problem

A wave travels along a stretched string. The string vibrates at 120 Hz and the distance between adjacent crests is 2.5 m. What is the wave speed?

Transverse wave on a string with wavelength 2.5 m labeled and propagation direction shownλ = 2.5 mAv = 300 m/s
Transverse wave on the string: wavelength λ = 2.5 m.

Given

  • f = 120 Hz

  • λ = 2.5 m

Find

Wave speed v.

Principle

A wave advances one wavelength per period, so speed equals frequency times wavelength.

Formula

Solution

  1. Write the wave equation: v=fλv = f\lambda

  2. Substitute: v=120×2.5v = 120 \times 2.5

  3. Calculate: v=300 m/sv = 300\ \mathrm{m/s}

300 m/s

Unit check

Hz × m = (1/s) × m = m/s. Matches speed.

What this means physically

Each crest races along the string at 300 m/s — nearly the speed of sound in air. Tighter or lighter strings carry waves even faster, which is how tuning works.

Common mistake

Mixing up frequency and period. If you are given T = 1/120 s instead, convert first: v = λ/T gives the same 300 m/s.