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.
What to measure
f in Hz; λ in m; v=fλ in m/s; T=1/f in s.
The idea underneath
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(x,t)=A sin(2πx/λ−2πft+φ); v=fλy, A, x, λ in m; t in s; f in Hz; φ is phase in radians.
Build the argument
- Write a travelling disturbance as y = A sin(kx − ωt + φ), with k = 2π/λ and ω = 2πf.
- Keeping phase constant gives v = ω/k = fλ. Add displacements, not amplitudes, when phases differ.
- Two waves travelling in opposite directions form nodes when their sum is zero for all times.
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.
Applications
The same language describes musical instruments, communications, seismic waves and interference-based measurement. Frequency content reveals structure hidden in a time trace.
Common misconception
The moving pattern is not the motion of a piece of the medium. Interference redistributes energy. A DFT has finite resolution and a Nyquist limit.
A further investigation
How can a wave move right while a material point moves up and down?
Check your understanding
At fixed v, doubling f makes λ…
- Half as large
- Twice as large
Explanation
λ=v/f. Local medium displacement differs from propagation: the disturbance transfers energy through space.
Model limits
Analytic linear educational model, not a numerical fluid solver. No damping, dispersion or nonlinear coupling.