The intensity of a certain sound at your eardrum is 0.0030 W/m^2. Calculate the rate P at which sound energy hits your eardrum. Assume that the area of your eardrum is about 51 mm^2.
I found this to be 1.53x10^-4 using I=P/A
What power output P0 is required from a point source that is 3.5 m away in order to create the same intensity at your eardrum?
What equation should be used here?
power /(4 pi r^2) = intensity
0.0030 W/m^2 = power/ (4 pi r^2)
Well, isn't your eardrum in for a treat! Let's calculate the power output P0 required from the point source!
We can use the inverse square law for this situation. According to this law, the intensity of sound decreases with the square of the distance. So, the equation we'll be using is:
I1/I2 = (r2^2)/(r1^2)
Where I1 is the intensity at your eardrum, I2 is the intensity at the point source, r1 is the distance from your eardrum, and r2 is the distance from the point source.
Now, we know that the intensity at your eardrum is 0.0030 W/m^2 and the distance from the point source is 3.5 m. We want to find P0, which is the power output needed to create the same intensity at your eardrum.
So, let's plug in the values and solve for P0:
0.0030 W/m^2 / I2 = (3.5m^2) / (r1^2)
Now, solving for I2:
I2 = 0.0030 W/m^2 / (3.5m^2 / r1^2)
You've already calculated the intensity at your eardrum, so let's substitute that in:
0.0030 W/m^2 / (3.5m^2 / r1^2) = 1.53x10^-4 W/m^2
And solving for P0:
P0 = I2 * A
Where A is the area of your eardrum, which is 51 mm^2. Converting mm^2 to m^2:
P0 = (1.53x10^-4 W/m^2) * (51 x 10^-6 m^2)
Now you can crunch the numbers and find the power output P0 required from the point source. Take it away, math whiz!
To calculate the power output (P0) required from a point source located 3.5 m away, we can use the equation for the intensity of sound from a point source:
I = P0 / (4πr^2)
where I is the intensity, P0 is the power output, and r is the distance from the source.
We can rearrange the equation to solve for P0:
P0 = I × 4πr^2
Plugging in the given values:
I = 0.0030 W/m^2 (the original intensity at the eardrum)
r = 3.5 m
P0 = 0.0030 W/m^2 × 4π(3.5 m)^2
Now we can calculate the power output required.
To calculate the power rate P at which sound energy hits your eardrum, we can use the equation P = I x A, where P is the power, I is the intensity of the sound, and A is the area of your eardrum.
The given intensity is 0.0030 W/m^2, and the area of your eardrum is 51 mm^2, which is equivalent to 0.000051 m^2.
Substituting these values into the equation, we get P = 0.0030 W/m^2 x 0.000051 m^2 = 1.53x10^-7 W.
Therefore, the rate P at which sound energy hits your eardrum is approximately 1.53x10^-7 watts.
To calculate the power output P0 required from a point source that is 3.5 m away in order to create the same intensity at your eardrum, we can use the inverse square law for sound intensity.
The inverse square law states that the intensity of a sound wave decreases inversely proportional to the square of the distance from the source.
The equation to calculate the required power output P0 is P0 = I x 4πr^2, where P0 is the power output, I is the intensity at the eardrum, and r is the distance from the source to the eardrum.
The intensity I at the eardrum is given as 0.0030 W/m^2, and the distance r is 3.5 m.
Substituting these values into the equation, we get P0 = 0.0030 W/m^2 x 4π(3.5 m)^2 = 0.553 W.
Therefore, the power output P0 required from a point source that is 3.5 m away to create the same intensity at your eardrum is approximately 0.553 watts.
I=P*A = .003*51*10^-6 watts not same as yours.
I=Io/distance^1
intensity decreases as distance ^2, fo Io=3.5^2 * I above