# Can the Firecracker Be Heard?

Can the Firecracker Be Heard?
Introduction: The decibel scale is logarithmic in intensity:

beta = 10log[I/I_0]
In this formula, I_0 is a reference intensity. To convert the intensity of sound waves from SI units to dB, I_0 is taken to be 10^{-12}W/m^2.

Once you know the intensity of a source in dB as measured at some reference distance, the intensity at a new distance can be found by subtracting the change in dB appropriate to the ratio of the new distance to the reference distance.

The change in dB corresponding to the change in distance may be found by replacing I_0 in the formula given here with the intensity at the reference distance and replacing I with the intensity at the new distance.

We apply the dB scale to a small firecracker that has an intensity of 140 dB at a distance of 1 m.

a.) The question asks: A child sets off the firecracker at a distance of 100 m from the family house. What is the sound intensity beta_100 at the house?
Express the sound intensity in decibels.

b.) Will the firecracker sound louder than the parents' conversation?