Ratio of Intensities of 2 sounds

[Irishdoug]

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?

 

[quinoa19]

From the definition, (ratios of) intensities should be "fed" to the log function, and decibels are what comes out. In your equations, the log function seems to be "fed" with the decibels...

 

[Irishdoug]

Sorry I don't quite follow?

 

[quinoa19]

On the last line, there are 130 and 60 decibels under the log function... Instead, according to definition, log function should be applied to intensities, and decibels produced as a result...

 

[RPinPA]

Suppose that a jet engine at 50 meters has a decibel level of 130...

Equation $L = \log(I/I_0)$ relates $I$ in W/m$^2$ to $L$ in dB. You're given a number in dB. So which variable in that equation are you being given?

 

[Irishdoug]

Thanks for replies. I'll give it another go tonight.