Question

An equation for loudness L in decibels is given by L= 10LogR where R is the sound’s relative intensity. An air-raid siren can reach 150 decibels and jet engine noise can reach 120 decibels. How many times greater is the relative intensity of the air-raid siren than that of the jet engine noise?

Answer 1

We are asked to find ratio of two relative intensities. Let's start by rearranging formula for R:
$L=10logR \\ logR= \frac{L}{10} \\ applying formula \\log_{a}b=c =\ \textgreater \ b= a^{c}\\R= 10^{\frac{L}{10}}$

For air-raid siren we have:
$R_{1}= 10^{\frac{150}{10}} =10^{15}$
For jet engine noise we have:
$R_{2}= 10^{\frac{120}{10}} =10^{12}$

To find out many times greater is the relative intensity of the air-raid siren than that of the jet engine noise we need to divide these two numbers:
tex] \frac{R_{1}}{R_{2}} = \frac{10^{15}}{10^{12}} =10^{3}=1000[/tex]