Initially, you hear the siren at 90 dB. When the distance between you and the ambulance is a quarter of what it was initially, at what intensity level do you hear the siren? Assume that the siren is emitting sound equally in all directions.
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To determine the intensity level when the distance between you and the ambulance is a quarter of the initial distance, we can use the inverse square law. According to the inverse square law, the intensity of sound decreases in proportion to the square of the distance.
In this case, let's say the initial distance between you and the ambulance is represented by "d". When the distance becomes a quarter of the initial distance, it will be represented as "d/4".
Since intensity decreases with distance squared, we can calculate the ratio of the initial intensity to the final intensity using the ratio of the distances squared:
Intensity ratio = (Initial distance / Final distance)²
= (d / (d/4))²
= 4²
= 16
This means that the intensity level decreases by a factor of 16 when the distance between you and the ambulance decreases to one quarter of the initial distance.
Now, we know that the initial intensity level is 90 dB. To find the intensity level when the distance is reduced to a quarter, we need to divide the initial intensity by the intensity ratio:
Final intensity = Initial intensity / Intensity ratio
= 90 dB / 16
= 5.625 dB
Therefore, when the distance between you and the ambulance becomes a quarter of the initial distance, the siren will be heard at an intensity level of approximately 5.625 dB.