How to play Wave Machine
- Choose a test and read the rope, the frequency, and the wavelength on the card.
- Use v = f·λ and T = 1 ÷ f; the wavelength is the distance from one crest to the next.
- Type your prediction and press Start. The motor fills the rope with waves in real time.
- Compare the orange marks with the crests on the rope, or with how far the waves get.
Wavelength, frequency, and period
Shake one end of a rope up and down steadily and a train of waves runs along it. The frequency f is how many shakes, and so how many waves, you make each second, measured in hertz (Hz). The period T is the time for one shake: T = 1 ÷ f, so 2 Hz means one wave every 0.5 s. The wavelength λ is the length of one wave, from one crest to the next. These are tied together by the wave speed. During one period the first wave moves exactly one wavelength before the next one leaves, so v = λ ÷ T = f·λ. The speed is set by the rope, by how tight and how heavy it is, not by your hand. So if you shake faster on the same rope, more waves fit in: the waves get shorter. And if you shake harder at the same rhythm, the waves get taller, but their speed and length stay the same. Watch any single point on the rope, like a bead: it goes up and down once each period.
A focused learning model
The rope is ideal: the waves keep their shape and speed and nothing is lost. The motor moves the end in a perfect sine, starting at rest; the front of the wave train moves out at the rope's speed, and nothing reflects from the far end. Heights are drawn larger than lengths. The amplitude has no effect on speed or wavelength, as for gentle waves on any real rope. Runs play in real time. Answers within 2% are right.