Answer:
![\mathbf{\beta=140\ dB}](https://img.qammunity.org/2022/formulas/mathematics/high-school/bd6v18lm206utnhtz5g0ufartuqt88wjla.png)
Explanation:
The Logarithm Function
The sound level is usually calculated as a logarithm by the formula:
![\displaystyle \beta=10\log(I)/(I_o)](https://img.qammunity.org/2022/formulas/mathematics/high-school/5wu41ru8vfdv6m7w3f0v3ay4239983mts9.png)
Where
I = Sound intensity in W/square meter
Io = Smallest sound intensity that can be heard.
![I_o=1\cdot 10^(-12)\ W/m^2](https://img.qammunity.org/2022/formulas/mathematics/high-school/7wq2xfuq65p6yjeytko6u0qa6qkrj72ujh.png)
The blue whale can emit a sound of I=106.8 W/square meter, thus the sound level is:
![\displaystyle \beta=10\log(106.8)/(1\cdot 10^(-12))](https://img.qammunity.org/2022/formulas/mathematics/high-school/rn6rhz3dqvaho99fqvz78vtkx2qlu1ccvx.png)
![\displaystyle \beta=10*14](https://img.qammunity.org/2022/formulas/mathematics/high-school/5oq0hu8te77178p5kbh5lsp5sa0gzxod83.png)
![\mathbf{\beta=140\ dB}](https://img.qammunity.org/2022/formulas/mathematics/high-school/bd6v18lm206utnhtz5g0ufartuqt88wjla.png)