Wave Speed
Speed of a wave from frequency and wavelength.
Formula
Variables
Example
A 340 Hz sound at λ = 1 m travels at v = 340·1 = 340 m/s.
How it works
This equation says that a wave’s speed depends on how many wave cycles pass each second and how long each cycle is. A higher frequency means more crests pass a point in one second, and a longer wavelength means each crest is spaced farther apart, so multiplying them gives the distance the wave travels per second. It comes from the basic idea that speed = distance ÷ time, with one wave cycle covering one wavelength in one period.
When to use it
Use this when you know a wave’s frequency and wavelength and need its speed, such as with sound, water waves, or light in a medium. It is also useful for rearranging to find frequency or wavelength when the other two quantities are known.
Worked example, step by step
A radio wave has frequency f = 95 MHz and wavelength λ = 3.16 m. Convert the frequency: 95 MHz = 95,000,000 Hz. Use v = fλ. Substitute: v = 95,000,000 × 3.16. Calculate: v = 300,200,000 m/s. Final answer: v ≈ 3.00 × 10^8 m/s.
Common mistakes to avoid
- Using the frequency in MHz or kHz without converting to hertz
- Mixing up wavelength units, such as using centimeters when the formula needs meters
- Assuming the wave speed changes just because frequency changes, even though the medium may set the speed
Did You Know?
Speed = frequency × wavelength holds for every wave — sound, light, and ocean swells alike.
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