Wave motion
What is wave speed?
Wave speed is the distance a wave disturbance travels per unit time. It depends on the properties of the medium and the type of wave.
Frequency describes how many complete cycles occur each second, while wavelength describes the distance between corresponding points on adjacent waves.
Main equation
Wave speed formula
Wave speedv = f × λ
- v is wave speed in metres per second.
- f is frequency in hertz.
- λ is wavelength in metres.
Rearranged equations
Calculate frequency or wavelength
Frequency
f = v ÷ λ
Divide wave speed by wavelength.
Wavelength
λ = v ÷ f
Divide wave speed by frequency.
Worked example
Calculate speed from frequency and wavelength
- Frequency is 170 Hz.
- Wavelength is 2 m.
- Apply v = f × λ.
- Substitute the values: v = 170 × 2.
- Wave speed is 340 m/s.
Inverse relationship
Frequency and wavelength
In the same medium, wave speed is normally constant. Increasing frequency therefore decreases wavelength, while decreasing frequency increases wavelength.
This inverse relationship is central to sound waves, water waves, electromagnetic radiation, and many laboratory experiments.
Unit guidance
Use compatible wave units
- Wave speed: metres per second (m/s).
- Frequency: hertz (Hz), equivalent to cycles per second.
- Wavelength: metres (m).
Convert centimetres, millimetres, kilohertz, megahertz, or other unit prefixes before entering values.
Applications
Where the wave equation is used
- Sound waves and acoustics.
- Water and mechanical waves.
- Radio and electromagnetic waves.
- Laboratory oscillation experiments.
- Communications and signal analysis.
Model limitations
Assumptions and limitations
The equation assumes a single wave travelling through a uniform medium under stable conditions. The entered frequency and wavelength must refer to the same wave.
Wave speed may change when the medium, temperature, tension, density, pressure, or other physical conditions change. Dispersive media can also produce different speeds for different frequencies.
Related tools
Continue your wave and motion analysis
Use the Average Speed Calculator for distance and elapsed-time calculations.
Use the Rotational Frequency Calculator to calculate frequency from revolutions and elapsed time.
Questions and answers
Wave speed calculator FAQ
What formula does the wave speed calculator use?
The calculator uses v = f × λ, where v is wave speed, f is frequency, and λ is wavelength.
How do I calculate wavelength?
Divide wave speed by frequency using λ = v ÷ f.
How do I calculate frequency?
Divide wave speed by wavelength using f = v ÷ λ.
What units should I use?
Use metres per second for wave speed, hertz for frequency, and metres for wavelength.
Does wave speed change when frequency changes?
In a fixed medium under unchanged conditions, wave speed is usually determined by the medium. Frequency and wavelength adjust inversely.