Question

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

$L(I_1)=10\log\frac{I_1}{I_0},L(I_2)=10\log\frac{I_2}{I_0}$ as $I_2=I_1/2$ then the loundness decreas is

$L(I_1)-L(I_2)=10(\log\frac{I_1}{I_0}-\log\frac{I_1}{2I_0})=10\log2\approx10\sdot0.301=3.01$ dB