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The loudness, L of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d , from the source of the sound. A person 15 feet from a jetski, it is 65 decibels loud. How loud is the jetski when the person is 41 feet away?

User Penguru
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Final answer:

The loudness of a sound is inversely proportional to the square of the distance from the source. Using the inverse square law, we can find the loudness of the jetski when the person is 41 feet away. Hence, it is approximately 8.7 decibels loud.

Step-by-step explanation:

To solve this problem, we can use the inverse square law for sound intensity. According to the law, the loudness of a sound is inversely proportional to the square of the distance from the source of the sound. In equation form, this can be written as:

L = k/d^2

where L is the loudness (in decibels), d is the distance (in feet), and k is a constant of proportionality.

We are given that when the person is 15 feet away from the jetski, it is 65 decibels loud. Let's use this information to find the value of k:

65 = k/15^2

k = 65 * 15^2 = 14625

Now we can use the value of k to find the loudness when the person is 41 feet away:

L = 14625/41^2

L = 8.7 decibels

So, when the person is 41 feet away from the jetski, it is approximately 8.7 decibels loud.

User Frapontillo
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