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 sound is emitted in a HEMIsphere, total area: 2PI(19.3)^2
assuming it is uniform, the amount just on the ear drum is...the ratio of the the areas of sound power per area.
W(above)*PI(1.7e-2 /2)^2 /(2 PI (19.3^2)) check that.
To calculate the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft, you can use the Inverse Square Law.
The Inverse Square Law states that the intensity of sound decreases with the square of the distance from the source. So, the sound power that reaches the eardrum is given by:
Power at eardrum = Power emitted × (1 / (4πr^2))
Where:
- Power at eardrum is the sound power that reaches the eardrum
- Power emitted is the sound power emitted by the jet aircraft (46673.5W, as calculated in Part One)
- r is the distance between the aircraft and the worker (19.3m)
Let's proceed with the calculations:
Power at eardrum = 46673.5W × (1 / (4π(19.3m)^2))
Power at eardrum = 46673.5W × (1 / (4π(373.49m^2)))
Power at eardrum = 46673.5W × (1 / (4 × 3.14159 × 139355.34m^2))
Power at eardrum ≈ 0.0241W
Therefore, the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft is approximately 0.0241W.
To calculate the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft, we need to use the concept of sound intensity. Sound intensity is the amount of sound power per unit area.
The formula for sound intensity is:
I = P / A
where I is the sound intensity, P is the sound power, and A is the area through which the sound is passing.
In Part One, we already calculated the sound power emitted by the jet aircraft, which is 46673.5 W.
Now, let's calculate the area through which the sound is passing. The area can be approximated as the surface area of a sphere with a radius of 19.3 m. The formula for the surface area of a sphere is:
A = 4πr^2
where A is the surface area and r is the radius.
Substituting the values, we get:
A = 4π(19.3)^2
Calculating this gives us:
A ≈ 4671.7 m^2
Now, to find the sound intensity, we divide the sound power by the area:
I = 46673.5 W / 4671.7 m^2
Calculating this gives us:
I ≈ 9.997 W/m^2
Since we now have the sound intensity, we can calculate the sound power that would strike the eardrum of the airport worker.
The formula for sound intensity is:
I = P / A
Rearranging the formula, we get:
P = I * A
Substituting the values, we get:
P = 9.997 W/m^2 * (π(1.7 × 10^(-2))^2)
Calculating this gives us:
P ≈ 9.997 W/m^2 * (π * 2.89 × 10^(-4))
P ≈ 3.046 × 10^(-3) W
Therefore, the sound power that would strike the eardrum of an airport worker 19.3 m from the aircraft is approximately 3.046 × 10^(-3) W.