Airplanes are noisy things. For example, if you stand really close to a runway, a military jet can produce a sound intensity of about 100 W/m^2 at a distance of 30 m from the plane (this is beyond painful noise). You live near a military airport and want to work on physics with your friend. Since you don't want to shout, you decide to find a spot far enough away from the airport that the airplane noise is below the threshold of conversation (10^{-6} W/m^2). How far do you need to go from the airport in kilometers to accomplish this?

300

precisely 299.99999999 by the formula I=P/r(pi)r^2 .

Thank you for the answer.

To calculate how far you need to go from the airport in kilometers to be below the threshold of conversation, we can use the inverse square law for sound intensity.

The inverse square law states that the intensity of sound decreases as the square of the distance from the source increases. Mathematically, it can be written as:

I₁/I₂ = (d₂/d₁)²

Where:
I₁ = initial sound intensity (100 W/m²)
I₂ = desired sound intensity for threshold of conversation (10⁻⁶ W/m²)
d₁ = initial distance from the source (30 m)
d₂ = desired distance from the source (unknown)

We can rearrange the equation to solve for d₂:

d₂ = √[(I₂/I₁) * d₁²]

Now, let's put the values into the equation and solve for d₂:

d₂ = √[(10⁻⁶ W/m²)/(100 W/m²) * (30 m)²]
= √[(10⁻⁶)/(100) * (30)²]
= √[(10⁻⁶)/(100) * 900]
= √(0.000009)
≈ 0.003 m

Since we want the distance in kilometers, we can convert 0.003 m to km:

0.003 m * 1 km/1000 m = 0.003 km

Therefore, you need to go approximately 0.003 kilometers (or 3 meters) away from the airport to be below the threshold of conversation.