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Topic $12$ HW

Can the Firecracker Be Heard?

$4$ of $16$

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Constants

Introduction

The decibel scale is logarithmic in intensity:

$=10$log$10$II$0$dB$=10$log$10$II$0$dB$.$

In this formula,$$I$0$I$0$is a reference intensity. To convert the intensity of sound waves from SI units to dB$,$I$0$I$0$is taken to be$1012$W$/$m$21012$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$$I$0$I$0$in the formula given here with the intensity at the reference distance and replacing$$II$$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$$$100$$100$at the house?

Express the sound intensity in decibels.

View Available Hint$($s$)$for Part A

$$dB

SubmitRequest$$Answer

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?

yes

no

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Incorrect. Incorrect; Try Again; $9$ attempts remaining. Feedback. Recall that the intensity varies as the inverse square of the distance. End of feedback.