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 solve this problem, we can use the inverse square law for sound intensity, which states that the intensity of sound decreases as the square of the distance from the source increases.

The formula for sound intensity in decibels (dB) is given as:

I(dB) = 10 * log10(I/I₀)

where I is the sound intensity in watts per square meter (W/m²) and I₀ is the reference intensity, which is 1 x 10^(-12) W/m².

We are given that the minimum intensity level the instrument can record is 30.9 dB. So, we can rearrange the formula to solve for the sound intensity:

I(dB) = 10 * log10(I/I₀)
I/I₀ = 10^(I(dB)/10)

Substituting the given minimum intensity level:

I/I₀ = 10^(30.9/10)
I/I₀ = 1000

Now, we can use the formula for sound intensity to calculate the maximum distance at which the animal will still be recorded. The formula is:

I = P/(4πr²)

where I is the sound intensity in watts per square meter (W/m²), P is the power of the sound source in watts (W), and r is the distance from the source in meters (m).

Rearranging the formula:

r = √(P/(4πI))

Substituting the given power of the sound source (0.0603 J/s) and the calculated sound intensity (1000 I₀):

r = √(0.0603/(4π*1000*1x10^(-12)))
r = √(0.0603/(4π*10^(-9)))
r = √(0.0603/4π) * 10^4

Using a calculator to evaluate the expression (√(0.0603/4π) * 10^4), we find:

r ≈ 0.0279 meters

Therefore, the maximum distance at which the animal will still be recorded is approximately 0.0279 meters.