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how are velocity and wavelength related
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Answered by
GPT-5 mini
AI
For a wave the basic relation is
v = f · λ
where
- v is the wave speed (m/s),
- f is the frequency (Hz),
- λ (lambda) is the wavelength (m).
You can rearrange: λ = v / f or f = v / λ.
In angular terms:
v = ω / k
with ω = 2πf (rad/s) and k = 2π/λ (rad/m).
Notes:
- The wave speed v depends on the medium (e.g., sound ≈ 343 m/s in air at 20 °C; light in vacuum c ≈ 3.00×10^8 m/s).
- In dispersive media different frequencies travel at different speeds; then phase velocity (v_phase = ω/k) and group velocity (v_group = dω/dk) can differ.
- For matter waves (de Broglie waves) the relations are similar in form, but the physical interpretation (phase vs. group velocity) needs care.
Example: A 440 Hz sound in air (v ≈ 343 m/s) has λ = 343 / 440 ≈ 0.78 m.
v = f · λ
where
- v is the wave speed (m/s),
- f is the frequency (Hz),
- λ (lambda) is the wavelength (m).
You can rearrange: λ = v / f or f = v / λ.
In angular terms:
v = ω / k
with ω = 2πf (rad/s) and k = 2π/λ (rad/m).
Notes:
- The wave speed v depends on the medium (e.g., sound ≈ 343 m/s in air at 20 °C; light in vacuum c ≈ 3.00×10^8 m/s).
- In dispersive media different frequencies travel at different speeds; then phase velocity (v_phase = ω/k) and group velocity (v_group = dω/dk) can differ.
- For matter waves (de Broglie waves) the relations are similar in form, but the physical interpretation (phase vs. group velocity) needs care.
Example: A 440 Hz sound in air (v ≈ 343 m/s) has λ = 343 / 440 ≈ 0.78 m.
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