Quick physics problem i need help with...

[djlightsout06]

A sinusoidal wave is travelingh along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0s. Also, a given maximum travels 425cm along the rope in 10.0s. What is the wavelength?

[AKG]

The wavelength is (among other things) the distance travelled by a given maximum in one period (one cycle of oscillation). You can find the period given the numbers you have. The period is the time taken for 1 cycle/vibration.

T = 30.0s/40.0 vibrations = 0.750 seconds/vibration

\lambda
= distance travelled/cycle
= distance travelled/second * seconds/cycle
= 4.25m/10.0s * 0.750s/cycle
= 0.31875 m/cycle
= 0.319 m (you don't really have to say, "/cycle")

so the wavelength (notice that it's only good to 3 significant digits) is 31.9 cm.