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Relation between intensity and amplitude

Now, the intensity I (``brightness'' in the case of light) of the pattern at the observation screen is a just a measure of the amount of energy arriving at each point tex2html_wrap_inline974 on the screen per unit time. In a real experiment, the screen is a two-dimensional surface. Thus, the precise measure we use for the intensity is the average energy arriving per unit time per unit area, or, simply, average power per unit area. To relate this to the solution for the waves tex2html_wrap_inline976 , we can generalize from the result we know for power on a string,

  equation50

It turns out that all phenomena (such as sound or light) which obey the wave-equation obey a very similar formula. The primary difference in going from waves on a string to any other type of wave is that the constant tex2html_wrap_inline978 (which measures the tension of the string) is replaced by some other constant characterizing the medium of propagation for the waves. If we consider traveling sinusoidal waves, then the solution will have the general form tex2html_wrap_inline980 . Then, using Eq. 1 we will find a result of the following form for the power. (Here, tex2html_wrap_inline982 indicates the average value of the quantity q.)

eqnarray58

Note that, at any instant in time t, the power may be different: it varies with the oscillations of tex2html_wrap_inline988 . This is why we define intensity as the time average of the arriving power. Finally, because the time average of tex2html_wrap_inline990 or tex2html_wrap_inline992 is just 1/2, we have

  eqnarray61

Note that in the last line we replaced the factor tex2html_wrap_inline996 with a general proportionality constant tex2html_wrap_inline998 . We do this because for waves which are not waves on a string, we end up with factors other than tex2html_wrap_inline978 to describe the medium of propagation. What is the same for all types of waves, the main point here, is that the intensity is proportional to the square of the amplitude.


next up previous contents
Next: Form of solution from Up: Pattern from a single Previous: Meaning of infinitesimal

Tomas Arias
Thu Sep 13 15:26:14 EDT 2001