The sound intensity 5.0 m from point source is 0.50 W/m².The power output of the source is: A)12.5 W B)39 W C)79 W D)160 W E)260 W

Question

Quizplus · Accepted Answer

The sound intensity (I) decreases proportionally to the square of the distance (r) from the point source, according to the inverse square law: 
I1/I2 = (r2/r1)^2

Using the given values: 
I1 = 0.50 W/m^2 
r1 = 5.0 m 
r2 = 1.0 m (since we want to find the power output at the source)

Therefore, I2 = I1 * (r1/r2)^2 = 0.50 W/m^2 * (5.0/1.0)^2 = 12.5 W/m^2

The power output (P) of the source can be found using the formula: 
P = I * A

where A is the surface area of a sphere with radius r2 = 1.0 m: 
A = 4πr2^2 = 4π

Therefore, P = I2 * A = 12.5 W/m^2 * 4π = 50π ≈ 157.08 W 
Rounding to the nearest whole number, we get the answer of 160 W.

The Sound Intensity 5