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
To determine the intensity level in W/m2 of the infrasound at different distances from the source, we can use the formula:
Intensity Level (dB) = 10 * log10(I / I0)
Where I is the intensity of the sound in W/m2 and I0 is the reference intensity, which is 1 x 10^-12 W/m2.
First, let's calculate the intensity level at a distance of 4 m from the source.
a) Intensity level at 4 m from the source:
Given: Intensity (I) = 106 dB, Distance (d) = 4 m
Intensity Level (dB) = 106 dB
Reference Intensity (I0) = 1 x 10^-12 W/m2
Now we can rearrange the formula to solve for I:
I = I0 * 10^(Intensity Level (dB) / 10)
Substituting the values into the formula:
I = (1 x 10^-12 W/m2) * 10^(106 dB / 10)
I = (1 x 10^-12) * 10^10.6
I ≈ 1 * 10^(-2)
I ≈ 0.01 W/m2
So, the intensity of the infrasound at 4 m from the source is approximately 0.01 W/m2.
b) Intensity level at 9 km from the source:
Given: Distance (d) = 9 km = 9000 m
We can use the same formula to calculate the intensity level at this distance, but first we need to find the new intensity at this distance. We can use the inverse square law for sound:
I2 = I1 * (d1 / d2)^2
Where I1 is the initial intensity, d1 is the initial distance, I2 is the new intensity, and d2 is the new distance.
Using the given values:
I1 = 0.01 W/m2 (from previous calculation)
d1 = 4 m
d2 = 9000 m
Substituting the values into the formula:
I2 = (0.01 W/m2) * (4 m / 9000 m)^2
I2 = 0.01 * (4 / 9000)^2
I2 ≈ 0.00000000001 W/m2
Now, we can calculate the intensity level at 9 km:
Intensity Level (dB) = 10 * log10(I2 / I0)
Substituting the values:
Intensity Level (dB) = 10 * log10(0.00000000001 / 1 x 10^-12)
Intensity Level (dB) = 10 * log10(0.00000000001 * 10^12)
Intensity Level (dB) = 10 * log10(0.01)
Intensity Level (dB) = 10 * (-2)
Intensity Level (dB) = -20 dB
Therefore, the intensity of the infrasound at 9 km from the source is -20 dB or approximately 0.00000000001 W/m2.