A loudspeaker at a rockconcert?

Question

generates 0.01 W/m^2 at 19 m at a frequency of 4 kHz. Assume the speaker spreads its enegy uniformly in 3 dimensions.

A) What is the total acoustic power output of the speaker in units of W?
B) At what distance will the intensity be at the pain threshold of 8 W/m^2 (in units of m)?
C) What is the intensity at 12 m (in W/m^2)?

Answer 1

1)a sphere of 19m radius has an
area of a = 3.1416*r^2 =3.1416*19^2 =1134 m^2
so the output is 0.01*1134 = 11.34W

Slight correction: Area of sphere = 4*pie*r^2
so the power output is 45W

Otherwise Excellent : )



2) Power inversely proportional to r^2.
The power must be 8/0.01 = 800 more than at 19m
the radius must be 19/28 =0.66m

3) 12m = 12/19 of the initial distance
the intensity must be (19/12)^2 =2.5 the initial value

the answer is 0.025 W/m^2

Answer 2

1) a sphere of 19m radius has an
area of a = 3.1416*r^2 =3.1416*19^2 =1134 m^2
so the output is 0.01*1134 = 11.34W

2) Power inversely proportional to r^2.
The power must be 8/0.01 = 800 more than at 19m
the radius must be 19/28 =0.66m

3) 12m = 12/19 of the initial distance
the intensity must be (19/12)^2 =2.5 the initial value

the answer is 0.025 W/m^2