An underwater micriphone is used to record sounds emitted by porpoises. The minimum intensity level the instrument can record is 30.9dB. Assuming a porpoise emits sound at a rate of 0.0603J/s, what is the maximum distance at which the animal will still be recorded? Neglect sound absorption in water and treat the porpoise as a point sound source.

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To determine the maximum distance at which the porpoise will still be recorded, we need to consider the relationship between intensity, distance, and power.

The intensity of a sound wave is defined as the power per unit area and is given by the formula:

I = P / (4πr²)

where I is the intensity, P is the power emitted by the sound source, and r is the distance from the source.

We are given the power emitted by the porpoise (P = 0.0603 J/s) and the minimum intensity level the instrument can record (30.9 dB). We first need to convert the intensity level from dB to standard units.

The formula to convert the intensity level from dB to standard units is:

I1 = I0 * 10^(L/10)

where I1 is the intensity in standard units, I0 is the reference intensity (10^(-12) W/m²), and L is the intensity level in dB.

Plugging in the values, we have:

I1 = 10^(-12) * 10^(30.9/10)
= 10^(-12) * 10^3.09
≈ 1.113 * 10^(-9) W/m²

Now, we can rearrange the formula for intensity to solve for the maximum distance (r):

r = sqrt(P / (4πI1))

Plugging in the values, we have:

r = sqrt(0.0603 / (4π * 1.113 * 10^(-9)))
= sqrt(0.0603 / (4 * 3.14159 * 1.113 * 10^(-9)))
≈ 16.107 meters

Therefore, the maximum distance at which the porpoise will still be recorded is approximately 16.107 meters.