Question

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

Answer 1

db = 10log(intensity of sound/threshold of human hearing)

Intensity = Power/Area

Intensity = Power/4 pie r^2

Power = Intensity x 4 x pie x r^2

equating power

Intensity(originally) x 4 x pie x r^2 = Intensity(at a distance 2r) x 4 x pie x (2r)^2
2r because he moves twice as far away


divide 4 x pie
lo intensity originaly, la intensity after moving
Io x r^2 = Ia x (2r)^2
Io = Ia x 4

lets say he was originally 1m, and moves to 2m
change in dB = dbo - dba = 10log(1/10^-12) - 10log(1/4 x 10^-12)
= 10log(4)
=6 db change

Answer 2

ive just realised i did it as if he starts close then moves twice as far away. the answer is exactly the same for if he started far away and then moves close.