KinexiaLEARN PHYSICS

Standing Waves — Violin String (Worked Example)

Easy
Problem

A violin string 0.33 m long has wave speed 280 m/s. What is its fundamental frequency?

Given

  • L = 0.33 m

  • v = 280 m/s

  • n = 1

Find

f₁.

Principle

f₁ = v/(2L) — shorter string, higher pitch than the guitar.

Formula

Solution

  1. Substitute: f1=280/(2×0.33)f_1 = 280/(2 \times 0.33)

  2. Denominator: 0.660.66

  3. Divide: f1=424 Hzf_1 = 424\ \mathrm{Hz}

424 Hz

Unit check

(m/s) ÷ m = Hz. The units confirm a vibration frequency, as required.

What this means physically

424 Hz — close to concert A (440 Hz); the player tunes by adjusting tension (which sets v). This is the open A string's neighbourhood.

Common mistake

Mixing up v and f. The 280 m/s is the wave speed on the string, not a frequency — it goes on top of the fraction.