Question

If the intensity of one sound is 7.24 x 10-4 W/m2 and the intensity of another sound is 6.31 x 10-3   W/m2, what is the difference of their sound intensity levels?

Answer 1

By definition, the intensity levels of both sounds are (respectively):

$$L_1 = 10\lg\left( \dfrac{I_1}{I_0} \right) \space dB\\ L_2 = 10\lg\left( \dfrac{I_2}{I_0} \right)\space dB$$

where $I_1 = 7.24\times 10^{-4}W/m^2$ is the inensity of the first sound, $I_2 = 6.31\times 10^{-3}W/m^2$ is the intensity of the second sound, and $I_0$ is some basic intensity.

The difference in levels is:

$$L_2-L_1 = 10\lg\left( \dfrac{I_2}{I_0}\right) - 10\lg\left( \dfrac{I_1}{I_0}\right) = 10\lg\left( \dfrac{I_2}{I_1}\right) \\ L_2-L_1 = 10\lg\left( \dfrac{6.31\times 10^{-3}}{7.24\times 10^{-4}}\right) \approx 9.4\space dB$$

Answer. $9.4\space dB$