If the intensity of a sound beam remains unchanged while the beam area is reduced in half, the power will also be Halved.
As intensity = Power / area
I1 = P1 / A1
I2 = P2 / A2
If I1 = I2 and A2 = A1 / 2
I = P1 / A1 I = P2 / (A1/2)
I = P1 / A1 I = 2 P2 / A1
P1 = I A1 P2 = I A1 / 2
P2 = P1 /2 = Halved
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