Question

14 identical cars are all honking their horns which a microphone measures to be 93.2 db. if only one car honks its horn, what sound intensity level will the microphone record? express you answer in db to 1 decimal place but do not include units in your answer. assume all cars are the same distance from the microphone. your answer:

Answer 1

To calculate the sound intensity level of one car honking its horn when 14 identical cars collectively produce 93.2 dB, we subtract 10 dB for each factor of 10 reduction in car numbers, resulting in approximately 81.7 dB for one car.

Step-by-step explanation:

When 14 identical cars are all honking their horns, and the combined sound intensity level is measured to be 93.2 dB, the sound intensity level recorded by only one car honking its horn can be calculated using the properties of the decibel scale. The decibel scale is logarithmic, not linear, meaning that for every increase of 10 dB, the sound intensity increases by a factor of 10. Therefore, to find the sound intensity level of one car, we need to use the equation ± 10 dB change corresponds to a factor of 10¹ in sound intensity.

Since 14 cars produce 93.2 dB, one car would produce 10 times less intensity per car. That would mean we subtract 10 dB for each factor of 10 reduction in the number of cars. Starting with 93.2 dB for 14 cars, reducing the number of cars to 1 car (1/14th of the original), we decrease by – 10 log10(14) dB. Thus:

Sound Intensity Level (one car) = 93.2 dB – 10 log10(14) ≈ 93.2 dB – 11.5 dB ≈ 81.7 dB

Therefore, the sound intensity level recorded by the microphone when only one car honks its horn is approximately 81.7 dB.