How to Calculate Wave Speed (v = fλ): Frequency × Wavelength

Calculate wave speed with v = fλ. Frequency vs wavelength, unit traps (Hz, cm), worked examples, and a free wave speed calculator.

What Wave Speed Asks

Wave speed tells you how fast a disturbance travels through a medium — the crest-to-crest progress along the rope, string, or air column — not how fast one particle on the wave wiggles up and down.

The core formula is v = f λ (v = f times lambda). Frequency f is how many waves pass per second (hertz). Wavelength λ is the length of one full cycle (metres). Their product is speed in metres per second.

If you already have f and λ (or v and one unknown), open the free wave speed calculator first, then return here for unit traps and the link to refraction.

The Formulas

  • v = f λ — wave speed from frequency and wavelength.
  • f = v / λ — rearrange for frequency.
  • λ = v / f — rearrange for wavelength.

    • In many intro problems the medium fixes v (sound in air ≈ 340 m/s, light in vacuum ≈ 3.0 × 10⁸ m/s). Then raising f shortens λ so that v = fλ still holds.

    Frequency, Wavelength, and Medium

  • Frequency is set by the source (how often it vibrates).
  • Wave speed is set mainly by the medium (tension, density, temperature).
  • Wavelength adjusts so v = fλ stays true for that medium.

    • When a wave crosses into a new medium and bends, use Snell's law — frequency usually stays the same while speed and wavelength change.

    Units

  • f → hertz (Hz). Convert kHz → Hz (× 1000).
  • λ → metres (m). Convert cm → m (÷ 100).
  • v → m/s.
  • Leaving λ in centimetres while expecting m/s is a classic exam trap.

    • Worked Examples

    Example 1: find wave speed

    f = 50 Hz, λ = 2.0 m. v = f λ = (50)(2.0) = 100 m/s.

    Example 2: find wavelength

    v = 340 m/s (approx. air), f = 170 Hz. λ = v/f = 340/170 = 2.0 m.

    Example 3: find frequency

    v = 3.0 × 10⁸ m/s, λ = 0.50 m. f = v/λ = 6.0 × 10⁸ Hz.

    Example 4: convert cm first

    f = 25 Hz, λ = 80 cm = 0.80 m. v = (25)(0.80) = 20 m/s. Using 80 m by mistake would give 2000 m/s.

    Common Mistakes

  • Leaving wavelength in centimetres while expecting m/s.
  • Using kHz as if it were Hz without converting.
  • Confusing wave speed with the oscillation speed of a particle.
  • Assuming v always changes when f changes — in many media v is fixed and λ adjusts.

    • Check It on the Calculator

    Wave speed calculator — v = fλ.

    Snell's law calculator.

    Velocity calculator for ordinary particle speed v = d/t.

    Learn v = fλ and confirm every homework number on the calculator.

    Articles

    • How to Calculate Electric Power (P = VI, I²R, V²/R)
    • How to Calculate Weight (W = mg): Mass vs Force
    • How to Calculate Density (ρ = m/V): Mass ÷ Volume
    • How to Calculate Acceleration (a = (v − u)/t)
    • How to Calculate Force (F = ma): Newton’s Second Law
    • How to Calculate Momentum (p = mv): Impulse & Conservation

    All articles · Browse all calculators