Hint: Find a way to express the function below in a better form.
The following equation describes a wave. Units have been omitted, but you may assume that all inputs/outputs are SI.
y(x,t) = 3e(-1x2+-4t2+4xt)
a.) Sketch the wave at t=0, and then find the following properties of this wave:
Height of the crest: ymax = 3
mand its location (at t=0): x = 0
mb.) Now unfreeze the wave from t=0 and find:
the wave's speed: 2
m/sand direction of travel: +x direction
c.) (NOT FOR CREDIT) Show that this wave obeys the wave equation, though it is not a periodic wave.
use the wave equation https://en.wikipedia.org/wiki/Wave_equation
ddx=1/v^2*ddt
take double derivatives and substitute point values, the double derivitave is quite messy. use wolfram alpha to cheat by doing a single derivative, then a second one. dx 3e(-1x2+-4t2+4xt) then a second one. then dt 3e(-1x2+-4t2+4xt) the direction could be found by graphing 3e(-1x2+-4t2+4xt) with various t values as constant, ex t=1,2,3
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