# Converting sound intensity to dB

## Homework Statement

The sound at a concert is measured to be 0.5 W/m^2. How many decibels is this?

## Homework Equations

β = 10ln(I/I_0)
I/I_0 = 10^(β/10)

## The Attempt at a Solution

I_0 = 1*10^-12 W/m^2
I = 0.5 W/m^2

Therefore,
β = 10ln(0.5/10^-12)
β = 269.378 dB

However,
.5/10^12 = 10^(β/10)
When using a TI-89 calculator to solve for β the answer comes to 116.99 dB, what I expected.

I can't find anything wrong with my work, but the dB level seems way too high for the first equation. I expected it should be somewhere around 115 dB. Why does the formula involving natural logs give the wrong answer?

ehild
Homework Helper
The sound intensity in dB is defined as 10*log10(I/I0).

ehild

The sound intensity in dB is defined as 10*log10(I/I0).

ehild

Nevermind, I thought log(x) was another way to write ln(x)... some research cleared this up. However, is there an easier way to find the log( function in the TI-89 calculator other than scrolling through the catalog?

Last edited:
ehild
Homework Helper
log(x)=ln(x)/ln(10). Calculate ln(I/I0) and divide by ln(10)=2.302.

ehild