Question A.9: A collection of four identical machines creates a decibel le...

We use the equation of decibel level to find the total sound intensity of the four machines, and then we divide by 4. From Equation (1):

87.0 dB =10 \log \left(\frac{I}{10^{-12} W / m ^{2}}\right)

Divide both sides by 10 and take the antilog of both sides, which means, equivalently, to exponentiate:

\begin{gathered}10^{8.7}=10^{\log \left(I / 10^{-12}\right)}=\frac{I}{10^{-12}} \\I=10^{-12} \cdot 10^{8.7}=10^{-3.3}=5.01 \times 10^{-4} W / m ^{2}\end{gathered}

There are four machines, so this result must be divided by 4 to get the intensity of one machine:

I=1.25 \times 10^{-4} W / m ^{2}