The sound intensity at a certain distance from a car is 2*10^-7 W/m^2.
- If the distance is tripled, what is the new intensity of the sounds?
- if the distance is halved, what is the new intensity of the sound?
for the first question I tried doing I2/2E^-7=3 since I'm assuming that's what the ratio (r2/r1)^2 would equal, but I'm getting an intensity that's bugger than the original and this doesn't make sense because it should be smaller since I'm farther away. I don't think I'm using the equation correctly, please help me.
If the distance is tripled, the intensity is 1/3^2 or 1/9 the original. If it is halved, the intensity is 2^2 or 4 times the original. Check my thinking.
oh, so, the original radius is 1 and you're dividing that by 3? but if you're 'halving' it, would it be 1 divided by 1/2?
correct me if I'm wrong, but for problems where I'm just told the distance is tripled, halved, etc, I take one. divide it by 3, 1/2, etc, and the square it?
To calculate the new intensity of sound when the distance is tripled or halved, you can use the inverse square law equation. The inverse square law states that the intensity of sound is inversely proportional to the square of the distance.
Let's start with the first question:
If the distance is tripled, the new distance is 3 times the original distance, which means r2 = 3r1.
To find the new intensity, we can use the inverse square law equation:
I2 = I1 * (r1^2 / r2^2)
Where:
I1 is the original intensity (2*10^-7 W/m^2)
I2 is the new intensity
r1 is the original distance
r2 is the new distance
Substituting the values into the equation:
I2 = (2*10^-7 W/m^2) * [(r1^2) / (3r1)^2]
Simplifying:
I2 = (2*10^-7 W/m^2) * (1 / 9)
I2 = 2*10^-8 W/m^2
Therefore, when the distance is tripled, the new intensity of the sound is 2*10^-8 W/m^2.
Now let's move on to the second question:
If the distance is halved, the new distance is half the original distance, which means r2 = (1/2) r1.
Using the same inverse square law equation:
I2 = I1 * (r1^2 / r2^2)
Substituting the values:
I2 = (2*10^-7 W/m^2) * [(r1^2) / ((1/2)r1)^2]
Simplifying:
I2 = (2*10^-7 W/m^2) * 4
I2 = 8*10^-7 W/m^2
Therefore, when the distance is halved, the new intensity of the sound is 8*10^-7 W/m^2.
I hope this explanation helps! Let me know if you have any further questions.