# Elephants communicate via infrasound, at frequencies as low as 11 Hz that can travel up to 9 km. The intensity of these sounds can reach 106 dB, measured a distance of 4 m from the source.

a) Determine the intensity level in W/m2 of the infrasound at 4 m from the source.

b) Determine the intensity level in W/m2 of the infrasound at 9 km from the source

Assume the sound energy radiates uniformly in all directions.

## To determine the intensity level in W/m2 of the infrasound at a certain distance, we can use the equation:

IL = 10 * log10(I/I₀)

where IL is the intensity level in decibels (dB), I is the sound intensity in watts per square meter (W/m2), and I₀ is the reference intensity, which is usually set to 10^(-12) W/m2.

a) To find the intensity level at 4 m from the source, we are given the intensity I as 106 dB at this distance. First, we need to convert 106 dB into sound intensity:

IL = 10 * log10(I/I₀)

106 dB = 10 * log10(I/I₀)

10.6 = log10(I/I₀)

10^(10.6) = I/I₀

I = 10^(10.6) * I₀

Next, we can calculate the intensity I:

I = 10^(10.6) * I₀ = 10^(10.6) * 10^(-12) W/m2

b) To find the intensity level at 9 km from the source, we need to apply the inverse square law, which states that the intensity of sound decreases as the square of the distance from the source increases. In other words, the intensity decreases inversely proportional to the distance squared.

We are given the intensity at 4 m, so we can use this as a reference to find the intensity at 9 km. Since the sound energy radiates uniformly in all directions, we can assume that the intensity is the same in all directions.

Using the inverse square law:

I₁/I₂ = (R₂/R₁)^2

where I₁ is the initial intensity (at 4 m), I₂ is the final intensity (at 9 km), R₁ is the initial distance (4 m), and R₂ is the final distance (9 km).

Plugging in the values:

I₁/I₂ = (4/9000)^2

Simplifying:

I₂ = I₁ / (9000^2 / 4^2)

Now, we can substitute the calculated initial intensity I₁ from part a) and solve for I₂:

I₂ = (10^(10.6) * 10^(-12)) / (9000^2 / 4^2)

This will give us the intensity in W/m2 at 9 km from the source.