The wave tank's next run is already decided: ripples with crests 3 cm above rest, spaced 2 m apart. Before the paddle starts, Cosmo's lab sheet asks for a picture of them: a bare grid, axes already labeled, and an order: draw the wave.
The ripples come first: real water, a real height, a real spacing. Reading graphs is done; now the routine runs in reverse. Two numbers in, one curve out.
Picture the real ripples first: crest tops 3 cm above the rest level, trough bottoms 3 cm below it, and each crest 2 m behind the next.
The lab sheet wants both of those facts in one drawing: how high the water swings, and how far apart the crests sit.
Mark the ceiling and the floor: the curve's crest tops will sit at +3 cm, its trough bottoms at -3 cm. The curve swings between plus and minus one amplitude.
Place the first crest anywhere convenient. Step one wavelength, 2 m here, along the position axis and mark the next crest: every crest sits one wavelength after the one before.
Halfway between two crests, mark a trough bottom at -3 cm: troughs sit half a wavelength after crests.
Join the marks with one smooth curve through the rest line, and check the finished sketch against both givens: crest height off the displacement axis, crest spacing along the position axis.
Construct a displacement-position graph of a wave with amplitude 3 cm and wavelength 2 m, first crest at 0.5 m. Where do the next crest and the first trough after it sit?
Crests sit one wavelength apart.
0.5 + 2 = 2.5
Troughs sit half a wavelength after crests, at minus one amplitude.
The half wavelength is 1 m, so the trough sits at 1.5 m, at -3 cm.
The next crest sits at 2.5 m (top at +3 cm), and the first trough sits at 1.5 m (bottom at -3 cm).
Beata constructs a displacement-position graph of a wave with amplitude 5 cm and wavelength 3 m, placing the first crest at 1 m. Enter the position, in m, of the next crest.
Cosmo constructs a displacement-position graph of a wave with wavelength 6 m, placing a crest at 1.5 m. Enter the position, in m, of the first trough after that crest.
Dilys's construction must show a wave with amplitude 3 cm. Between which displacement values should her curve swing?
A construction task gives wavelength 5 m, with the first crest placed at 2 m. Enter the position, in m, of the next crest.
A construction task gives wavelength 3 m, with a crest placed at 1.2 m. Enter the position, in m, of the first trough after that crest.
Anselm's finished graph must show a wavelength of 6 m, but his crest tops sit 3 m apart. Which fix makes the graph correct?