A baseball coach shouts loudly at an umpire standing 3.6 meters away.
If the sound power produced by the coach is 2.2×10−3 W, what is the intensity of the sound when it reaches the umpire? Answer in units of W/m2.
Well, if we assume that the umpire has decent hearing and isn't wearing earplugs, let me calculate that for you.
Let's start with the fact that intensity is defined as power per unit area. So, we need to find the area of a sphere with a radius of 3.6 meters, using the formula A = 4πr^2.
Now, we'll plug in the radius and calculate the area.
A = 4π(3.6)^2 = 162.86 m^2.
Since we're given the sound power, we can divide it by the area to find the intensity.
Intensity = 2.2×10−3 W / 162.86 m^2
Now, let me grab my calculator...
Well, it seems that the intensity of the sound when it reaches the umpire is approximately 1.35×10−5 W/m^2.
To determine the intensity of the sound when it reaches the umpire, we can use the formula:
Intensity = Power / Area
But first, we need to calculate the area over which the sound is spreading. Assuming the sound spreads out equally in all directions, we can consider the area of a sphere:
Area = 4πr^2
Given that the umpire is standing 3.6 meters away from the coach, the radius of the sphere would be 3.6 meters.
Now, let's calculate the area:
Area = 4π(3.6)^2
= 4π × 3.6^2
≈ 162.86 m^2
Now, we can calculate the intensity:
Intensity = Power / Area
= 2.2 × 10^(-3) W / 162.86 m^2
≈ 1.35 × 10^(-5) W/m^2
Therefore, the intensity of the sound when it reaches the umpire is approximately 1.35 × 10^(-5) W/m^2.
To find the intensity of the sound when it reaches the umpire, we can use the inverse square law for sound propagation. According to the inverse square law, the intensity of sound decreases as the square of the distance from the source increases.
The formula for the intensity of sound is given by:
I = P / A
Where:
I is the intensity of sound (in W/m^2),
P is the sound power (in W), and
A is the area through which the sound is spreading (in m^2).
In this case, we have the sound power P = 2.2 × 10^(-3) W and the distance between the coach and the umpire d = 3.6 meters.
Since the sound is spreading equally in all directions, we can assume that it spreads in a spherical shape. Therefore, the area of the sphere can be calculated using the formula:
A = 4πr^2
Where r is the distance between the coach and the umpire.
Substituting the values into the equation:
A = 4π(3.6)^2 = 4π(12.96) = 162.38 m^2
Now, we can calculate the intensity using the formula:
I = P / A = 2.2 × 10^(-3) / 162.38 ≈ 1.355 × 10^(-5) W/m^2
Therefore, the intensity of the sound when it reaches the umpire is approximately 1.355 × 10^(-5) W/m^2.