Question

A dog barks with an intensity level of 80 decibels. Two barking dogs produce what intensity level?

Answer 1

We are given that a dog barks with an inetensity level of 80 dB and asked to find out the intensity level produced by two barking dogs.

The combined intensity level of both dogs is the sum of each dog's intensity level.

$\begin{gathered} I_{net}=I_1+I_2 \\ I_{net}=2I_{} \\ I_{net}=2\cdot I_0\cdot10^{\frac{\beta}{10}}_{} \end{gathered}$

Where β is 80 dB and I0 is the reference intensity (1x10^-12 W/m^2)

$\begin{gathered} I_{net}=2\cdot10^{-12}\cdot10^{\frac{80}{10}}_{} \\ I_{net}=2\cdot10^{-12}\cdot10^8_{} \\ I_{net}=2\cdot10^{-12+8} \\ I_{net}=2\cdot10^{-4} \end{gathered}$

The net β is given by

$\begin{gathered} \beta_{\text{net}}=10\log (\frac{I_{net}}{I_0}) \\ \beta_{\text{net}}=10\log (\frac{2\cdot10^{-4}}{10^{-12}}) \\ \beta_{\text{net}}=10\log (2\cdot10^{-4+12}) \\ \beta_{\text{net}}=10\log (20^8) \\ \beta_{\text{net}}=10(8.301) \\ \beta_{\text{net}}=83\; dB \end{gathered}$

Therefore, two barking dogs produce 83 dB intensity level.