Library / Foundations: Physics / FPH-14
Foundations: Physics
Wave speed
Speed of a wave from frequency and wavelength.
- Ref
- FPH-14
- Rev
- v1
- Field
- Foundations: Physics
- Result
- v [m/s]
Use frequency f in Hz and wavelength λ in m for wave speed in m/s. Period T is the time for one cycle.
A wave’s speed equals how many cycles pass each second times the length of each cycle.
Calculator
m/s
Hz
m
- Period2.273 ms
- Wavelength at 3×10⁸ m/s speed681,800 m
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Wave speed (m/s) current value 343.2 m/s
fFrequencyKey driver
0.78780,000
λWavelength
0.4444,000
- Sound in air travels about 340 m/s and radio waves 3×10⁸ m/s.
- At a fixed speed, higher frequency means shorter wavelength.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| f Frequency | 1 to 1,000,000 Hz | 0.78 | 780,000 | 780,000 | +10% | +10 % |
| λ Wavelength | 0.001 to 100 m | 0.44 | 44,000 | 44,000 | +10% | +10 % |
Sweep of Frequency
| Frequency (Hz) | Wave speed (m/s) |
|---|---|
| 1 | 0.78 |
| 5.623 | 4.386 |
| 31.62 | 24.67 |
| 177.8 | 138.7 |
| 1,000 | 780 |
| 5,623 | 4,386 |
| 31,620 | 24,670 |
| 177,800 | 138,700 |
| 1,000,000 | 780,000 |
Sweep one variable
Wave speed (m/s)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
v
Wave speed
What the equation gives you. Everything else feeds it.
f
Frequency
Cycles per second. Directly proportional.
λ
Wavelength
Length of one cycle. Directly proportional.
Worked example with the values above
- Frequency 440 Hz, wavelength 0.78 m.
- Multiply: 440 × 0.78.
- v = 343.2 m/s.
Assumptions and limits
- Wave medium unchanged.
- Frequency stays the same when the wave changes medium.
Common mistakes
- Using kHz without converting to Hz.
- Confusing wavelength with amplitude.
Statistics and uncertainty
Measuring λ from a short length of wave (a few crests) gives a larger relative error than measuring across many wavelengths.
Where it is used
- Radar and radio wavelength from frequency.
- Acoustic ranging.
Maths you need
- Frequency: cycles per second
- Wavelength: distance between crests