Question

1. The amplitude, or loudness, of certain sound waves in a recording studio can be measured by the equation L(I)=10log(II0). L(I) is measured in decibels and is the intensity of a barely audible sound (about watts per square meter), and I is the actual intensity2. If a sound's intensity is half the original value, by how many decibels does the loudness decrease? Round your answer to the nearest hundredth.

Answer 1

$L(in \ dB)=10 \ log\frac{I}{I_o}$

As per the question,$I=\frac{I_o}{2}$ And substituting it in above equation,

$L(in \ dB)=10 \ log\frac{I_o}{2I_o}=10 \ log\frac{1}{2}$ $=-3.010$

This will be the change in the loudness level.