- #1

Irishdoug

- 102

- 16

## Homework Statement

The decibel scale of loudness is L = 10 log##\frac{I}{Io}## where I, measured in watts per square meter, is the intensity of the sound and Io= ##10^-12## watt/m 2 is the softest audible sound at 1000 hertz. Classical music typically ranges from 30 to 100 decibels. The human ear's pain threshold is about 120 decibels.

Suppose that a jet engine at 50 meters has a decibel level of 130, and a normal conversation at 1 meter has a decibel level of 60. What is the ratio of the intensities of the two sounds?

## Homework Equations

L = 10 log ##\frac{I}{Io}## where Io is ##10^{-12}## and I is the intensity of the sound in square meters.

## The Attempt at a Solution

Let I1 be intensity of jet engine and I2 intensity of converstaion.

log##\frac{I1}{Io}##/ ##\frac{I2}{Io}## = log##\frac{I1}{Io}## - log##\frac{I2}{Io}##

= log##\frac{130}{10^-12}## - log##\frac{60}{10^-12}##

I thought this would give correct answer however it did not. The correct answer is 13 - 6 = 7, s0 ##\frac{I1}{I2} =## ##10^7##

I then tried plugging in numbers in various ways but cannot get the correct answer. ANy idea what I have done wrong?