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Waves & Optics Formula

What is Wave Speed?

Wave speed equals frequency times wavelength — valid for all wave types.

Formula: v = f\lambda

Plain-English Meaning

All waves — sound, light, water — obey this rule. Frequency (f) is how many waves pass per second (in Hz). Wavelength (λ) is the distance from one crest to the next. Multiply them and you get how fast the wave moves.

If a waves question feels messy, sketch the geometry or phase relationship first, then return to the algebra.

Deeper Explanation

v = fλ = ω/k. For light in vacuum: c = fλ (constant). For sound in air: v ≈ 343 m/s at 20°C. Phase velocity v_p = ω/k; group velocity v_g = dω/dk (speed of energy/information). In dispersive media v_p ≠ v_g.

Worked Example

Problem: A sound wave in air has frequency 440 Hz (concert A). Find its wavelength (v = 343 m/s).

  • v = fλ → λ = v/f
  • λ = 343/440 = 0.780 m

Result: λ ≈ 0.78 m

At A Glance

Category: Waves & Optics

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.