Elephants communicate via infrasound, at frequencies as low as 14 Hz that can travel up to 10 km. The intensity of these sounds can reach 103 dB, measured a distance of 5.0 m from the source. Determine the intensity level of the infrasound 10 km from the source, assuming the sound energy radiates uniformly in all directions.
I2/I1 = R1^2/R2^2 = 5^2/(10^4)^2
= 25 * 10^-8
10 log (25*10^-8) = 10 [-8 + 1.4]
= - 66 dB
103 - 66 = 37 dB
still pretty loud
To determine the intensity level of the infrasound 10 km from the source, we can use the inverse square law, which states that the intensity of a sound wave decreases as the square of the distance from the source increases.
First, let's define the variables:
- I1: intensity of the sound at the distance of 5.0 m from the source (given as 103 dB)
- I2: intensity of the sound at the distance of 10 km from the source
- d1: initial distance from the source (given as 5.0 m)
- d2: final distance from the source (given as 10 km)
To calculate the intensity level at a different distance using the inverse square law, we will use the formula:
I2 = I1 * (d1/d2)^2
Given that:
I1 = 10^(103/10) (converting decibels to intensity)
d1 = 5.0 m
d2 = 10 km = 10,000 m
Now let's plug in the values and calculate I2:
I2 = 10^(103/10) * (5.0/10,000)^2
Calculating this using a calculator:
I2 = 10^(10.3) * (5.0/10,000)^2
= 1995.262 * (5.0/10,000)^2
= 1995.262 * (0.00025)
= 0.4988155
The intensity level at a distance of 10 km from the source is 0.4988155.
Note: When we talk about intensity level, it is usually measured in decibels (dB), but in this case, since we are working with intensity as the unit of measurement, the calculated value is not in decibels.