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# Listening to two pure tones with the same sound pressure levels but with increasing frequency separation, what happens to the loudness?

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- nyphdinmdLv 76 months ago
Let's call p1 = P0*cos(w1*t) and p2 = P0*cos((w1+w)*t) where 0 <= w

When both waves hit a surface the resulting pressure is

p(t) = p1 + p2 = P0*(cos(w1*t) + cos((w1 +w)*t) = P0*(cos(w1*t) + cos(w1*t)*cos(w*t) - sin(w1*t)*sin(w*t))

p(t) = P0*cos(w1*t)*{1 + cos(w*t) - cot(w1*t)*sin(w*t)}

when w = 0, then p(t) = 2*P0*cos(w1*t)

when w > 0, the loudness varies as the two terms with w*t can vary.

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