A loudspeaker emits energy in all direction at the rate of 1.5 J/s. What is the intensity level at a distance of 20m?
That sound energy is not spread over an area of the entire area.
I assume you are considering a hemisphere.
1.5/(2PI(20^2) J/m^2 s
To find the intensity level at a distance of 20m, we can use the formula for intensity:
Intensity = Power / (4πr^2)
Where:
- Power is the rate of energy emitted, given as 1.5 J/s
- r is the distance from the loudspeaker, given as 20m
Now let's plug in the values and calculate the intensity level at a distance of 20m:
Intensity = 1.5 / (4π × 20^2)
Simplifying further:
Intensity = 1.5 / (4 × 3.14159 × 400)
Intensity ≈ 1.5 / 502.6548
Intensity ≈ 0.002981 J/m^2
Therefore, the intensity level at a distance of 20m is approximately 0.002981 J/m^2.
To find the intensity level at a distance of 20m from the loudspeaker, we need to use the formula:
Intensity Level (in decibels) = 10 * log10 (I/Io)
Where:
- Intensity Level is the level of sound intensity in decibels (dB)
- I is the sound intensity at the given distance
- Io is the reference intensity level
First, let's calculate the sound intensity (I) at a distance of 20m from the loudspeaker.
The sound intensity decreases with the square of the distance from the source, so we can use the inverse square law equation for sound intensity:
I = Io / (4πr²)
Where:
- I is the sound intensity at a distance r from the source
- Io is the initial sound intensity emitted by the loudspeaker
- r is the distance from the source to the point of interest
Given:
- Io = 1.5 J/s (sound intensity emitted by the loudspeaker)
- r = 20m (distance from the loudspeaker)
Substituting the values into the equation:
I = 1.5 J/s / (4π * (20m)²)
Now let's calculate the intensity level using the intensity we just found.
Intensity Level (in decibels) = 10 * log10 (I/Io)
Substituting the values:
Intensity Level = 10 * log10 (I / 1.5 J/s)
Calculate the value inside the logarithm, and then take the logarithm and multiply it by 10 to get the final result.
Using these steps, you can calculate the intensity level at a distance of 20m from the loudspeaker.