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Wave intensity

  1. Jan 24, 2006 #1
    the wave intensity is defined as the squared wave amplitude.

    [tex]I(z,t)=A^2 (z,t)[/tex]
    [tex]A(z,t)=a cos [2 \pi (\frac{r}{\lambda}-\frac{t}{T})][/tex]

    the wavelength is 10cm
    period is 1/10s
    a=1mm


    1. what is the instantaneous intensity at r=15cm and t=.5s?

    is the solution:
    [tex]A^2(z,t)=(.1 cos [2 \pi (\frac{15}{10}-\frac{.5}{.1})])^2[/tex]

    2. what is the average intensity averaged over a long time at that location?

    [tex]\int A^2(15,t)=\int_{0}^{\inf} (.1 cos [2 \pi (\frac{15}{10}-\frac{t}{.1})])^2 dt[/tex]

    is that how I would solve #2?
     
  2. jcsd
  3. Jan 24, 2006 #2

    mezarashi

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    Homework Helper

    Integrating like that would give you a total sum. You need to divide it by the time to get the 'average'. A trick would be to integrate from 0 to any T (period of the wave) and divide it by T.
     
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