Application of Logarithmic Models with Decibel Scale

Question

If the intensity of a sound from one source is 1,000 times that of another, how much more is the decibel level of the louder sound than the quieter one?

Answer 1

 

Calculating sound intensity as measured in dB utilizes the formula  dB = 10*log( Intensity / 10^-12). Ignoring the denominator, since it applies to both the louder and quieter sounds:

 

If the two sounds are represented by 1 and 1000, their relative intensities in dB are:

 

Quieter Sound = 10 * log (1) dB      =   0 dB

Louder Sound =  10 * log (1000) dB = 30 dB 

 

The Louder Sound is   (30- 0) dB  =  30 dB higher