Waves, explained.
A wave carries a disturbance. In a transverse wave, a medium particle moves perpendicular to the direction of propagation. One wavelength separates neighboring crests, and frequency counts cycles per second.
The relationship to remember
Key formulas
- Wave speed
- v = fλ
- Frequency × wavelength
- Period
- T = 1/f
- Time for one complete cycle
- Wavelength
- λ = v/f
- Distance between neighbouring crests
- Traveling sine wave
- y = A sin(2π(x/λ − ft))
- Moves in the +x direction
Worked example
Problem. Ocean swell arrives at a beach every 8.0 s, and the crests are 100 m apart. What are the frequency and the wave speed?
- The period is T = 8.0 s, so the frequency is f = 1/T = 1/8.0 = 0.125 Hz.
- Wave speed: v = fλ = 0.125 × 100 = 12.5 m/s.
Answer. The swell has a frequency of 0.125 Hz and travels at 12.5 m/s.
A quick check
A frequency of 0.5 Hz and wavelength of 4 m give wave speed 2 m/s and period 2 s.
Inside the default experiment
- Wave speed = frequency × wavelength = 0.5 × 4 = 2 m/s.
- Period = 1/f = 2 s.
- Particle displacement is y = 1 sin(2π(x/4 − 0.5t)).
When this model applies
An ideal transverse sinusoidal wave. Frequency and wavelength are independently set; wave speed changes with their product.
Make a prediction. Then test it.
Track the orange particle. Does it travel along with the wave?
Try it: Traveling wave simulator ↗Frequently asked questions
Wondering about the why? Start here.
Does increasing amplitude make the wave faster?
Not in this ideal model. Speed is set by fλ; amplitude changes the size of the displacement.
Can frequency and wavelength vary independently in a real medium?
In a nondispersive medium with fixed wave speed, their product stays constant. This explorer allows both inputs so you can compare the resulting speeds.