if concorde registers at 128dB and another aeroplane registers at 94 dBwhat is their combined loudness?...

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- Jun 14th 2007, 04:14 AM #1

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- Jun 14th 2007, 04:29 AM #2
The long way first:

$\displaystyle 128 = 10 log_{10} \left ( \frac{I_1}{I_0} \right )$

(where $\displaystyle I_0$ is the reference level, the value of which at the moment escapes me, but we don't need a value for it anyway.)

$\displaystyle \frac{I_1}{I_0} = 10^{12.8}$

$\displaystyle I_1 = I_0 \cdot 10^{12.8}$

For the second sound

$\displaystyle 94 = 10 log_{10} \left ( \frac{I_2}{I_0} \right )$

etc.

$\displaystyle I_2 = I_0 \cdot 10^{9.4}$

So

$\displaystyle I_1 + I_2 = I_0 (10^{9.4} + 10^{12.8})$

So the "loudness" will be:

$\displaystyle 10 log_{10} \left ( \frac{I_0(10^{9.4} + 10^{12.8})}{I_0} \right ) $

$\displaystyle = 10 log_{10} (10^{9.4} + 10^{12.8}) \approx 128.002 \, dB$

I have corrected the above calculation (thanks again to CaptainBlack). The result is still practically the same as my original result in that it would be VERY difficult to hear the 94 dB sound as it barely contributes compared to the 128 dB sound.

-Dan

- Jun 14th 2007, 08:12 AM #3

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- Jun 14th 2007, 08:55 AM #4

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- Jun 15th 2007, 04:08 AM #5

- Jun 15th 2007, 04:25 AM #6

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- Jun 18th 2007, 04:34 AM #7

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## ok.....

ok i sort of got that..bt disreguarding the fact if u can or cannot hear certain things.....what actualy is the combined loudness if u did add both sounds together....

the sounds being...

concorde registering 120dB

and

an aeroplane registering 94dB?

- Jun 18th 2007, 05:53 AM #8