Final answer:
To determine the distance you are standing from the sound source, we can use the formula for intensity and the given values of 50 dB and 32 dB. Rearranging the formula and simplifying, we find that the ratio of intensities is 0.001. Using the relationship between intensity and distance, we can determine that you are standing at a distance that is approximately 0.032 times the initial distance from the sound source.
Step-by-step explanation:
To determine the distance you are standing from the sound source, we need to use the concept of sound intensity. The difference in sound intensity between the source and your ear can be calculated using the formula:
Intensity (dB) = 10 * log10(I1/I2)
By plugging in the given values of 50 dB and 32 dB, we can rearrange the formula to find the ratio of intensities. Rearranging the formula gives us:
I1/I2 = 10^((32 - 50)/10)
Simplifying the equation gives us:
I1/I2 = 10^(-18/10) = 0.001
The intensity of sound decreases with distance, so the ratio of intensities is also equal to the square of the ratio of distances:
(Distance1/Distance2)^2 = I1/I2 = 0.001
Therefore, (Distance1/Distance2)^2 = 0.001, and taking the square root of both sides, we get:
Distance1/Distance2 = √0.001 = 0.032
So, you are standing at a distance that is approximately 0.032 times the initial distance from the sound source.