Maximum intensity of two nearly equal-frequency waves with beats

[JuanYsimura]

Homework Statement

For two equal-amplitude waves of nearly equal frequencies w+d/2 and w-d/2 (at a fixed position x), you have shown that the intensity exhibits \beats"
which for d = 2pi Hz can be perceived directly by the ear, even though the
main frequency is perceived only through the signal processing of the auditory
nerve. How does the maximum intensity compare to the sum of the maximum
intensities of either wave separately?

Homework Equations

The Attempt at a Solution

So, I wrote both waves as: y1 = ACos[xk+t(w+d/2)], y2 = ACos[xk'+t(w-d/2)]. Adding them together yields: Y = y1 + y2 = 2Acos[{x(k-k')+d}t/2]cos[{x(k+k')+2tw}t/2]. So I am not really sure what it means to find the maximum intensity? Do I have to find the maximum intensity for y1 and y2 separately, and then find the mx intensity for Y? Can someone give me a hint on how to solve this problems. Thanks.

 

[diazona]

Yeah, pretty much. You find the intensities of y1, y2, and Y, and then compare them, i.e. is the intensity of Y larger, smaller, the same...?