Waves
Phase Velocity
Velocity at which the phase of a wave propagates through space.
Variables
vpm/s
Phase velocity
Speed of phase propagation
Allowed values: greater than 0
ωrad/s
Angular frequency
Radians per second
Allowed values: greater than 0
krad/m
Wave number
Radians per meter
Allowed values: greater than 0
Derivation
From wave equation y = A sin(kx - ωt), phase velocity v_p = ω/k = fλ.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- ω = 2 rad/s (Angular frequency)
- k = 3 rad/m (Wave number)
Result: vp = 0.66666667 m/s
Other waves formulas with the same quantities
- Angular Frequency (Wave Properties) shares Angular frequency
- SHM Displacement (Simple Harmonic Motion) shares Angular frequency
- SHM Velocity (Simple Harmonic Motion) shares Angular frequency
- SHM Acceleration (Simple Harmonic Motion) shares Angular frequency
- SHM Maximum Velocity (Simple Harmonic Motion) shares Angular frequency
- SHM Total Energy (Simple Harmonic Motion) shares Angular frequency
Where this formula is listed
- Waves formulas, under Wave Properties, alongside Period and Frequency, Wave Intensity, Intensity-Amplitude Relation, Inverse Square Law (Intensity) and Wave Speed on String.
- In the waves list it comes after Group Velocity and before Speed of Sound in Gas.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Phase Velocity formula?
Phase Velocity is written v_p = ω/k. Velocity at which the phase of a wave propagates through space. It belongs to Waves, under Wave Properties.
What are the units in v_p = ω/k?
In SI units, v_p is phase velocity, measured in m/s; ω is angular frequency, measured in rad/s; k is wave number, measured in rad/m.
How is the Phase Velocity formula derived?
From wave equation y = A sin(kx - ωt), phase velocity v_p = ω/k = fλ. The result is v_p = ω/k.