波速和波長

Start with the Wavelength guide on the stage and the source and probe graph below it. The guide marks one crest-to-crest spacing in space, while the graph shows how the source point and one downstream probe repeat in time. These are two views of the same wave: the probe is showing the same oscillation later, after the disturbance has had time to travel through the medium.

Now change Wave speed while keeping Wavelength fixed. The crest pattern crosses the ruler faster, the source and probe traces complete each cycle in less time, and the Delay guide shrinks because the same distance is covered more quickly. Instead, keep Wave speed fixed and increase Wavelength. The crests spread farther apart, fewer cycles fit into each meter, and the source frequency falls.

The phase-map graph turns that timing idea into a distance picture. Every extra wavelength of downstream distance adds one full cycle of lag, so a probe one wavelength farther away returns to the same phase, just one period later. Moving the probe does not change the wave being launched. It only changes the delay and phase difference between the source and that location.

That is why v = f lambda is so useful: spacing, timing, and travel must all agree. The same relation later helps explain sound arrival delays, interference, and standing waves. Next, keep the probe fixed and compare a pure Wave speed change with a pure Wavelength change, then move the probe by one full wavelength and check that the phase repeats while the delay increases.