Wavelength, frequency and speed.

Step 1 of 5

What travels

In the Unit on oscillations you saw a body repeat the same motion again and again about its point of equilibrium. A wave is an oscillation that passes on: each bit of the medium oscillates, and pushes its neighbour to oscillate after it.

The Scene is a ripple tank, a tray of shallow water. A small bead on a vibrating arm taps the surface again and again, and each tap sends out a ring that moves away from it. Don’t watch the rings; watch one spot of water: it rises when a crest arrives, sinks when a trough arrives, and does it again. Time in the Scene runs $8$⁠ times slower than real, and the waves are drawn taller than they are, so you can follow them.

Step 2 of 5

The wavelength

Choose On under Show the crests: each crest is marked with a bright line. The distance from one crest to the next is the wavelength, $\lambda$⁠ (lambda).

The bead taps $f$⁠ times a second: that is the frequency, in hertz. In the time between one tap and the next, one cycle, the crest before moves on exactly one wavelength. So in a whole second, $f$⁠ cycles, the wave covers $f$⁠ wavelengths:

$v = f\lambda$⁠

Frequency and Wave speed are fixed now. The numbers are real: ripples in water a few millimetres deep travel at about 25 cm/s, as they do in a classroom ripple tank.

Step 3 of 5

The period

The period $T$⁠ is the time between two crests passing the same spot, like the period of a pendulum or a spring. As there, it is the frequency turned over:

$T = \frac{1}{f}$⁠

In each period the crest moves on one wavelength, so the same rule can also be written $v = \dfrac{\lambda}{T}$$v =$$\dfrac{\lambda}{T}$⁠.

Step 4 of 5

Tapping faster

What sets each of the three numbers? The source sets the frequency: one tap, one crest. The water sets the speed: in the Scene, deeper water gives faster waves. The wavelength is what is left, $\lambda = \dfrac{v}{f}$$\lambda =$$\dfrac{v}{f}$⁠.

Wave speed is fixed now, because the water does not change. Predict what will happen when the bead taps faster, then look.

Step 5 of 5

Deeper water

Now the Frequency is fixed and Wave speed is free: changing it is like filling the tank with more water or less. Find the speed that gives the wavelength asked for.

Try it: after checking, move Amplitude. The crests are lower or taller, but the gaps between them do not move: the amplitude sets how much energy the wave carries, not how fast it travels.

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