01 · How fast does a wave travel?
At fixed speed, what happens to wavelength as frequency rises?
Predict crest spacing when frequency doubles.
- Select the travelling wave.
- Hold propagation speed fixed and change frequency.
- Follow the distance a crest travels in one complete cycle.
Measurement
f in Hz; λ in m; v=fλ in m/s; T=1/f in s.
Frequency counts cycles per second; wavelength is the distance a crest travels in one cycle. Amplitude is maximum displacement from equilibrium. In this nondispersive model, changing frequency changes wavelength without changing propagation speed.
y, A, x, λ in m; t in s; f in Hz; φ is phase in radians.
y(x,t)=A sin(2πx/λ−2πft+φ); v=fλ
Worked example 1
For v=4 m/s and f=2 Hz, λ=2 m and T=0.5 s.
Worked example 2
At the same v=4 m/s, f=4 Hz gives λ=1 m.
How can a wave move right while a material point moves up and down?
Assumptions
Analytic linear educational model, not a numerical fluid solver. No damping, dispersion or nonlinear coupling.