Let's conduct a simulated experiment using the applet below. Click "Play" and record the time taken for the wave to cover a distance that is equal to its wavelength.
It can be observed that, as a wave moves, it covers a distance of one wavelength over one period. Hence, the relationship between speed of wave, wavelength and period is given as $$v=\dfrac{\lambda}{T}$$
As frequency is the inverse of period or $f = \dfrac{1}{T}$, $$v=f\lambda$$
Since the speed of a wave in a homogeneous medium is a constant, changing the frequency changes the wavelength of the wave too, following the relationship $v = f \lambda $ as seen in the simulation below. Observe the animation of the two graphs representing a wave. The displacement-distance graph, when animated, shows the movement of an entire wave while the displacement-time graph represents the movement of a single particle (represented with a red dot) over time.