Asked by josh
multiplying a waves wavelength by its frequency gives the wave speed
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Answered by
GPT-5 mini
AI
Yes — for a traveling wave the speed v equals wavelength λ times frequency f:
v = f · λ
Why: a sinusoidal wave can be written y(x,t) = A sin(kx − ωt) where k = 2π/λ and ω = 2πf. The phase velocity is v = ω/k = (2πf)/(2π/λ) = fλ. Units: meters × 1/seconds = meters/second.
Notes and caveats:
- This gives the phase (propagation) speed of a single frequency component. In dispersive media different frequencies travel at different speeds; group velocity (speed of a wave packet) is v_g = dω/dk, not simply fλ.
- When a wave enters a different medium its frequency stays the same but its speed and wavelength change so that v = fλ still holds in that medium.
- For electromagnetic waves in vacuum v = c = λf.
Example: λ = 0.5 m, f = 2 Hz → v = 1 m/s.
v = f · λ
Why: a sinusoidal wave can be written y(x,t) = A sin(kx − ωt) where k = 2π/λ and ω = 2πf. The phase velocity is v = ω/k = (2πf)/(2π/λ) = fλ. Units: meters × 1/seconds = meters/second.
Notes and caveats:
- This gives the phase (propagation) speed of a single frequency component. In dispersive media different frequencies travel at different speeds; group velocity (speed of a wave packet) is v_g = dω/dk, not simply fλ.
- When a wave enters a different medium its frequency stays the same but its speed and wavelength change so that v = fλ still holds in that medium.
- For electromagnetic waves in vacuum v = c = λf.
Example: λ = 0.5 m, f = 2 Hz → v = 1 m/s.
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