a very loud train whistle has an acoustic power output of 100 W. if the sound energy spreads our spherically, what is the intensity level in dB at a distance of 100 meters from the train? I0=10^(-12)
the answer is 200 m but how do i get it?
How can the intentity level be in meters?
oooh...sorry I meant to write 89.0 dB
To find the intensity level in dB at a distance of 100 meters from the train, we can use the formula:
IL = 10 * log10(I / I0)
Where IL is the intensity level in dB, I is the intensity of the sound wave, and I0 is the reference intensity.
First, we need to calculate the intensity of the sound wave at a distance of 100 meters from the train. Since the sound energy spreads spherically, the intensity decreases as it propagates from the source.
The relationship between intensity and distance is given by the inverse square law, which states that the intensity is inversely proportional to the square of the distance:
I1 / I2 = (D2 / D1)^2
Where I1 and I2 are the intensities at distances D1 and D2 respectively.
In this case, the initial distance is not given, so we can assume it is at a very close distance to the train, where the sound energy is spread evenly in all directions. Thus, we can use the given acoustic power output of 100 W to calculate the initial intensity.
Since power is the rate at which energy is transferred, we can use the formula:
Power = Intensity * Area
Where Power is the acoustic power output, Intensity is the initial intensity, and Area is the surface area of the sphere at a distance of 100 meters. The formula for the surface area of a sphere is:
Area = 4 * π * r^2
Given the radius (distance) r is 100 meters, we can now calculate the initial intensity:
Intensity = Power / Area
Next, we can calculate the final intensity at a distance of 100 meters using the inverse square law formula:
Final Intensity = Initial Intensity * (Initial Distance / Final Distance)^2
Assuming the initial distance is very small compared to the final distance, we can use the initial distance as 1 meter.
Now that we have the final intensity, we can substitute it into the formula for the intensity level in dB to get the answer.
The sound is spread over an area of 4PI*100^2 in m^2
The intensity then is in watts/m^2=
100/(4PIE4)=7.96E-4 watts/m^2
db= 10 log (7.96E-4 /10^-12)