Question

During takeoff, the sound intensity level of a jet engine is 170 dB

dB at a distance of 32 m

m . What is the sound intensity level at a distance of 1.0 km

km?

Answer 1

As we know, sound power is inversely proportional to distance:

$$I_2=I_1r_1^2/r_2^2.$$

Find the sound power at 32 m:

$$B_1=10\log\frac{I_1}{I_0}=170,\\\space\\ \frac{I_1}{I_0}=10^{17}→I_1=I_0·10^{17}=(10^{-12})10^5\text{ W/m}^2.$$

Substitute this into the very first equation:

$$I_2=10^5·32^2/1000^2=102.4\text{ W/m}^2.$$

Sound intensity level that corresponds to 102.4 W/m²:

$$B=10\log\frac{102.4}{10^{-12}}=140\text{ dB}.$$