Part One:
The decibel level of the noise from a jet aircraft
is 130 dB when measured 19.3 m from
the aircraft.
How much sound power does the jet aircraft
emit?
Answer in units of W - 46673.5W
I need help with Part Two:
Part Two:
How much sound power would strike the
eardrum of an airport worker 19.3 m from
the aircraft? (Assume the diameter of the
worker’s eardrum is 1.7 × 10−2m)
the power is evenly distributed over the surface of a sphere with a radius of 19.3 m
46673.5 W / (4 π 19.3^2) m^2
calculate watts/m^2
calculate the area of the eardrum
FYI ... be aware of significant figures
It says this is incorrect
what is incorrect?
When I plug in the answers to that equation and do the work the quest says thats incorrect
have you learned about significant figures
did you notice the FYI
yes, the quest does not care about significant figures
see my response above. I have an issue with the sphere on a Jet)
130 dB is equivalent to 10 w/m^2
the area of the eardrum is ... π r^2 = π (8.5E-3)^2 m^2 = 2.27E-4 m^2
10 w/m^2 * 2.27E-4 m^2 = 2.27E-3 W = 2.27 mW (milliwatts)
To solve Part Two, we need to determine the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft. We can use the inverse square law for sound intensity to calculate this.
The inverse square law states that the intensity of sound decreases with the square of the distance from the source. Mathematically, it can be represented as:
I = P / (4πr^2)
Where I is the intensity, P is the power, and r is the distance from the source.
From Part One, we know that the sound power emitted by the jet aircraft is 46673.5 W.
Using this information, we can calculate the sound intensity at a distance of 19.3 m from the aircraft:
I = 46673.5 W / (4π(19.3 m)^2)
Simplifying this expression:
I ≈ 46673.5 W / (4 * 3.14159 * (19.3 m)^2)
I ≈ 46673.5 W / (4 * 3.14159 * 373.49 m^2)
I ≈ 46673.5 W / (4 * 3.14159 * 139738.9201 m^2)
I ≈ 46673.5 W / (1756602.8307 m^2)
I ≈ 0.0266 W/m^2
Now, we can find the sound power striking the worker's eardrum by multiplying the calculated intensity by the area of the eardrum.
Area of eardrum = π (1.7 × 10^(-2) m / 2)^2
Area of eardrum ≈ π (0.0085 m)^2
Area of eardrum ≈ 0.0227 m^2
Sound power striking the eardrum = intensity * area of eardrum
Sound power striking the eardrum ≈ 0.0266 W/m^2 * 0.0227 m^2
Sound power striking the eardrum ≈ 0.000602 W
Therefore, the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft is approximately 0.000602 W.