3. If the whistle has a sound intensity of 90 dB when the boat passes you 7 m away, how loud (in dB) is it in the cockpit just 1 m from the whistle

630dB

Explanation:

First you must know that the relationship between the sound intensity and the distance is an inverse relationship.

Let I represent the sound intensity

d represent the distance

Since I is inversely proportional to d, hence;

I ∝ 1/d

I = k/d

k is the constant of proportionality

If the whistle has a sound intensity of 90 dB when the boat passes you 7 m away, this means;

when I = 90dB, d = 7m

Substitute and get k first;

I = k/d

90 = k/d

k = 90 * 7

k = 630

To get how loud (in dB) is it in the cockpit just 1 m from the whistle, we will find I when d = 1 m

From the expression I = k/d

k = 630, d = 1

I = 630/1

I = 630dB

Hence the intensity is 630bB loud in the cockpit when it is just 1m from the whistle.

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