What approximate change in decibles does an observer experience form a sound source if the oberver moves to a new location that is 67% as far from the source?
To determine the approximate change in decibels experienced by an observer when they move to a new location, we can use the inverse square law for sound intensity.
The inverse square law states that the intensity of sound decreases as the square of the distance from the source increases. Mathematically, this relationship can be expressed as:
I1 / I2 = (d2 / d1)^2
Where:
- I1 is the initial sound intensity
- I2 is the final sound intensity
- d1 is the initial distance from the sound source
- d2 is the final distance from the sound source
In this case, since the observer moves to a new location that is 67% (or 0.67) the distance from the sound source, we can substitute these values into the equation:
I1 / I2 = (0.67)^2
Simplifying this equation, we have:
I1 / I2 = 0.4489
To find the difference in decibels, we can convert the intensity ratio to decibels using the formula:
ΔdB = 10 * log10(I1 / I2)
Plugging in the value of I1 / I2, we get:
ΔdB = 10 * log10(0.4489)
Calculating this, we find:
ΔdB ≈ -4.51 dB
Therefore, the approximate change in decibels experienced by the observer is -4.51 dB when they move to a new location that is 67% as far from the sound source.