Question

So i have the solution for this problem, but my questions is that when they were finding the sound intensity level where did they get the initial intensity? ( 1 × 10−12)

A speaker with a power of 58 W is playing music. What is the sound intensity level of the music at a distance of 22 m? Assume that the sound can only be heard in front of the speaker and not behind it.

Solution: In order to find the sound intensity level, first the intensity must be calculated. Since the sound only goes in front of the speaker, the area is half of the surface area of a sphere, which is 2πr2 . The intensity is found by: I = Power Area = Power 2πr2 = 58 2π(22)2 = 1.907 × 10−2 W/m2

The sound intensity level is given by: β = (10 dB) log10 I I0 = (10 dB) log10 1.907 × 10−2 1 × 10−12 = (10 dB) log10(1.907 × 1010) = (10 dB)(10.28) = 102.8 dB

Answer 1

That is not Initial intensity.

It is a reference Intensity, Io = 1*10^-12 W/m^2.

This is the lowest Intensity value that human can hear sound.