A sound wave has an
intensity of 0.32 W/m^{2} at a distance r from the source. If the
distance is increased by 0.5m, the sound level is decreased by 2.0 dB.
Assume the loudspeaker emits sound in all directions. Find the distance r.

a. The distance r = m

The intensity I of sound is related to the sound level b through the relationship:

where I_{0} is the reference
intensity = 10^{-12} W/m^{2} (for

I = 10^{-12} W/m^{2},
b =
0). We can
calculate the sound level
b_{
}at the
location r_{1} using the above relation:

The sound level at the location r_{2}
= r_{1 }+ 0.5 m is b_{2
}given by

Answer

We know that since
the power P of the source is constant, that is P_{1} = P_{2},

But

2-5 Intensity and sound level

Example 2