Question

What is the decibel level of a dog barking with intensity 10−5 watts per square inch? Use a logarithmic model to solve.

Answer 1

Answer:

The sound intensity is about 101.9 dB

Step-by-step explanation:

Sound intensity is the amount of sound energy per unit area.

The intensity of the dog bark is 10⁻⁵ W/in². The intensity of sound in decibels is given by:

$\beta=10\ dB*log(\frac{I}{I_o} )\\\\Where\ I=Sound\ intensity\ in \ W/m^2, I_o=reference\ sound\ intensity=10^{-12}\ W/m^2\, \beta= sound\ intensity\ in\ dB$

I = 10⁻⁵ W/in² = 0.0155 W/m²

Therefore:

$\beta=10\ dB*log(\frac{I}{I_o} )\\\\\beta=10\ dB*log(\frac{0.0155}{10^{-12}} )\\\\\beta=101.9\ dB$

The sound intensity is about 101.9 dB