Can the Firecracker Be Heard? The decibel scale is logarithmic in intensity: =10

Question

Can the Firecracker Be Heard?

The decibel scale is logarithmic in intensity:

=10log10II0dB.

In this formula, I0 is a reference intensity. To convert the intensity of sound waves from SI units to dB, I0 is taken to be 1012W/m2.

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 I0 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.

Part A

A child sets off the firecracker at a distance of 100 m from the family house. What is the sound intensity 100 at the house?

Express the sound intensity in decibels.

dB

The child's parents are inside the house talking. A typical house attenuates (reduces the intensity of) outside sounds by a factor of around 40 dB--more at high frequencies (when double-pane windows are closed) and less at low frequencies. Also, a typical conversation has an average sound level of 65 dB.

Part B

Will the firecracker sound louder than the parents' conversation?

Will the firecracker sound louder than the parents' conversation?

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Explanation / Answer

Part A)   the sound intensity at distance 100 m =    140 - 20log(100/1)

                                                =   100 dB

Part B)    Here,    firecracker sound inside house = 100 - 40 = 60 dB

=>     No,   the firecracker sound is not louder than the parents' conversation

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