Question

jim halves the distance between himself and a sound source. What is the change of decibels of the sound he hears?

Answer 1

6.02dB

Step-by-step explanation:

The sound level intensity can be calculated by using the formula:

`I(dB)=10log_(10)((I)/(I_o))`

where Io is the threshold of human hearing, and I is the intensity of the sound in at a certain distance. I is given by

`I=(P)/(4\pi r^2)`

where P is the power of the source and r is the distance to the source. By replacing I in the expression for I(dB) we obtain

`I(dB)=10log((P)/(4\pi r^2I_o))=10log((P)/(\pi r^2I_o))-10log(4)`

when jim halves the distance we have r'=1/2r:

`I'(dB)=10log((P)/(4\pi ((1)/(2)r)^2I_o))=10log((P)/(\pi r^2I_o))`

Hence, the change o decibels is:

`I'-I=10log(4)=6.02dB`

hope this helps!!