The formula
- Wave speed
v = fλ- Speed from wavelength and period
v = λ / T- Frequency and period
f = 1 / T
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
v | Wave speed through the medium | m/s |
f | Frequency, the number of waves passing a point each second | Hz (1 Hz = 1 s⁻¹) |
λ | Wavelength, the length of one complete wave | m |
T | Period, the time for one full oscillation | s |
When it applies
- Any periodic wave: sound, light, ripples on water, or a wave traveling along a string.
- The medium is uniform. Speed changes only where the medium changes, and then the frequency stays fixed while the wavelength adjusts.
- Frequency in hertz and wavelength in meters, so that the speed comes out in meters per second.
Worked example
Problem. A guitar string vibrates at 440 Hz. If sound travels through the room at 343 m/s, what is the wavelength of the note in air?
- The string sets the frequency of the sound wave it launches, so f = 440 Hz.
- The speed belongs to the air, not to the string: v = 343 m/s at ordinary room temperature.
- Rearrange v = fλ into λ = v / f = 343 / 440.
- λ = 0.7795 m, which is 0.78 m to two significant figures.
Answer. The wavelength in air is about 0.78 m.
Common mistakes
- Assuming a louder or higher-pitched source makes the wave travel faster. Neither amplitude nor frequency changes the speed in a given medium.
- Changing the frequency when a wave crosses into a new medium. The frequency is fixed by the source, and the wavelength is what adjusts.
- Leaving the wavelength in centimeters while the speed is in meters per second.
- Treating period and frequency as the same quantity. They are reciprocals.
Related formulas
- Kinematics equations:
v = v₀ + at - Snell's law:
n₁·sin θ₁ = n₂·sin θ₂