## Illustration 17.2: Wave Functions

Please wait for the animation to completely load.

A traveling wave is shown in black at time t = 0 seconds (**position is given in meters**). Three sliders are given that change certain properties of the wave. Restart. In general, we would write the wave function for a right-moving wave as

y(x,t) = A cos (k x - ω t + φ) = A cos ( (2π/λ) x - (2 π/T) t+ φ).

However, we are looking at the wave at t = 0 and we cannot determine the wave speed or frequency (where v = λ f = ω/k), so we just have:

y(x,t) = A cos (k x + φ) = A cos ((2π/λ) x + φ).

Which slider changes which quality of the wave? Well, there are three sliders and three parameters in the wave function. Try each slider and see what happens. Slider A controls the phase shift, φ, since it shifts the function to the left or right. Slider B controls the wavelength of the wave and therefore the wave number k, since k = 2π/λ. Clearly Slider C controls the amplitude, A, of the wave function.

If what was discussed above has made sense, you should be able to identify the wave parameters (find the value of the phase shift, wavelength and amplitude) using the sliders for this wave function (shown in red).

Illustration authored by Mario Belloni.

Script authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.