Wavefunction of a transverse wave

A transverse wave on a string is created by moving one end up and down in simple harmonic motion. The string is shown as a series of pieces. One particular piece is colored red so that you can easily track its motion.

This animation begins with the wave already in motion at t=0.

The wavefunction that describes the motion of a piece of the string at position x is given by

y(x,t)=Asin((2π/λ)x-(2π/T)*t +φ)

where the phase φ is zero for this example. Measure the wavelength and period of the wave. Measure the x-position of the red piece. Use the information to write an equation for y(t) for the red piece.

Check your answer by typing the function for y(t) in the box. Click the Start Animation link to see your function plotted on the graph, along with the actual function for y(t) for the red piece.

Note: that the function y(t) depends on the piece of the string at position x. Thus, the functions y(t) for two different pieces of the string are not necessarily the same.