The Sound Scale

Table of Contents

Loudness of Sound

dB from Intensity

$db=10log(\frac{I}{I_o})$ $d{b}_1-d{b}_2=10log(\frac{I}{I_o})$

Intensity from dB

$\frac{I_1}{I_2}=10^{\frac{(d{B}_1-dB2)}{10}}$ There is a 10 because its in decibels. if its in bels, then we dont need the 10(s) $10^{-12}$ is the softest sound Each successive increment of 10db is 10x louder than the previous. 20db is 10x as loud as 10db

Scale

120 dB is threshold of pain. blood will flow out your ears 85dB is hearing damage after 8 hours

Examples

1. How many times more intense is the sound of piano at 67dB to a whisper of 22dB $10^{\frac{67-22}{10}}$ = $10^{4.5}$
2. two 80dB phones. do they add up to 160dB? YES? NO? Convert everything to an intensity. You cant add dB, but you can add intensities $80=10log(\frac{I}{I_o})$ $8=log(\frac{I}{I_o})$ $10^8=\frac{I}{I_o}$ $10^8(I_o)=I$ $2I=2(10^8)(I_o)$ $dB=10\log (\frac{2(10^8)(I_o)}{I_o})$ $dB=10\log (\frac{2(10^8)}{1})$ $dB=83.01$