By how many decibels does the sound intensity from a point source decrease if you increase the distance to it by a factor 6?
To calculate the decrease in sound intensity in decibels (dB) when the distance to a point source is increased, we can use the inverse square law for sound propagation. According to this law, the sound intensity decreases by a factor of the square of the distance change.
Here's how you can calculate it step by step:
1. Determine the distance factor: The question states that the distance is increased by a factor of 6. This means the new distance is 6 times larger than the original distance.
2. Square the distance factor: To find the decrease in sound intensity, square the distance factor obtained in the previous step. In this case, 6 squared is equal to 36.
3. Convert the distance factor to decibels: To convert the distance factor to decibels, use the following formula:
Decibels = 10 * log10(distance factor)
In this case, the distance factor is 36, so the calculation would be:
Decibels = 10 * log10(36)
4. Calculate the decibels: Using a calculator (or a logarithm table), find the logarithm base 10 of 36 and multiply the result by 10.
Decibels ≈ 10 * 1.5563
Rounding to the nearest decimal place, we get:
Decibels ≈ 15.6 dB
Therefore, the sound intensity from the point source decreases by approximately 15.6 decibels when the distance is increased by a factor of 6.