v = fλ Formula – Wave Speed Practice
v = fλ — Wave speed from frequency and wavelength
Wave speed equals frequency times wavelength: v = f λ. Rearrange to f = v/λ or λ = v/f. Period relates by f = 1/T.
Guide — how to use this formula
- 1. Use SI: Hz and metres for m/s.
- 2. v = fλ, or rearrange for f or λ.
- 3. If given period: f = 1/T first.
- 4. Crest travel distance: d = v t after finding v.
Derivation
In one period T a wave advances one wavelength λ, so speed is λ/T:
- With f = 1/T:
v = f\lambda - Rearrangements:
f = \frac{v}{\lambda},\quad \lambda = \frac{v}{f}
Convert cm → m and kHz → Hz before substituting.
Examples
Example: 10 Hz, λ = 2 m
v = 20 m/s.
Example: find λ
v = 340 m/s, f = 170 Hz → λ = 2 m.