A speaker creates uniformly spherical sounds w/ 500 watts of power a)What is the

Question

A speaker creates uniformly spherical sounds w/ 500 watts of power

a)What is the intensity, I, of the sound at a distance of 20 meters from the speaker? What is the sound intensity level, , of the sound at a distance of 20 meters from the speaker?

b) What is the intensity, I, of the sound at a distance of 10 meters from the speaker? What is the sound intensity level, , of the sound at a distance of 10 meters from the speaker?

c) How many deciBels do you increase walking from 20 meters away from the speaker to 10 meters away from the speaker?

c) What power output would the speaker have to put out in order to create 100 dB at a distance 20 meters from the speaker?

Explanation / Answer

here,

sound intensity, I = (Power)/(4*pi*r^2)
also
dB = 10*log(I/10^-12)

part a:
distance, r = 20 m

Intensity, I = 500 /(4*pi*20^2)
Intensity, I = 0.99 watt/m

db = 10*log(0.99/10^-12)
db = 119.956 db

part b:
distance, r = 10 m

Intensity, I = 500 /(4*pi*10^2)
Intensity, I = 0.398 watt/m

db = 10*log(0.398/10^-12)
db = 116 db

part c:
increase in db = 119.956 - 116
increase in db = 3.956 db

part d:
Since,

intensity, I = e^(dB/10) * 10^-12
intensity, I = e^(100/10) * 10^-12
intensity, I = 2.203*10^-8 watt/m^2

So,
power, P = I * 4 * pi * r^2
power, P = 2.203*10^-8 * 4 * pi * (20)^2
power, P = 1.107*10^-5 watts

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