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How can I convert decibels to pressure units, such as PSI, or vice versa? I've seen formulas such as dB = 10*log (P/Pref) or 20*log(V/Vref). Is this correct? How do I know what the reference P is? Thanks for your help!

- Justin

Justin wrote:How can I convert decibels to pressure units, such as PSI, or vice versa? I've seen formulas such as dB = 10*log (P/Pref) or 20*log(V/Vref). Is this correct? How do I know what the reference P is? Thanks for your help!

If P is power, the 10*log form is correct. However if P is pressure, db = 20*log(P/Pref) and Pref is 20 uPa (micropascals, I can't make a "mu" here). The assumption is that P is an rms pressure value, any static (dc) pressure is ignored. A 10 dB increase is always 10X in power or energy, but power is proportional to power, or to the square of voltage or pressure. That is where the factors of 10 or 20 come from.

Note that 20 Pa is 120 dB, painfully loud, while static atmospheric pressure is 101.325 kPa.

http://www.eie.fceia.unr.edu.ar/~acusti ... undlev.htm

For electrical signals, you have to find a reference to what the reference level is, but 1 mW of power (frequently into 600 ohms), or 1 V are common ones.

- Guest

Use this equation:

dB = 20*log( a/b )

where

a = the measured sound level in Pascals

b = 2*10^-5

to test; use a = 2 Pascals and you should get 100 dB

dB = 20*log( a/b )

where

a = the measured sound level in Pascals

b = 2*10^-5

to test; use a = 2 Pascals and you should get 100 dB

- Guest

Guest wrote:Justin wrote:How can I convert decibels to pressure units, such as PSI, or vice versa? I've seen formulas such as dB = 10*log (P/Pref) or 20*log(V/Vref). Is this correct? How do I know what the reference P is? Thanks for your help!

If P is power, the 10*log form is correct. However if P is pressure, db = 20*log(P/Pref) and Pref is 20 uPa (micropascals, I can't make a "mu" here). The assumption is that P is an rms pressure value, any static (dc) pressure is ignored. A 10 dB increase is always 10X in power or energy, but power is proportional to power, or to the square of voltage or pressure. That is where the factors of 10 or 20 come from.

Note that 20 Pa is 120 dB, painfully loud, while static atmospheric pressure is 101.325 kPa.

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For electrical signals, you have to find a reference to what the reference level is, but 1 mW of power (frequently into 600 ohms), or 1 V are common ones.

-----

Nice response, however, the original question asked how to convert dB to PSI. That can be done as follows:

Knowns:

20 Pascals = 120 dB (as define above)

1 psi = 6894.757 Pascals

Therefore:

120 dB / 20 Pa = 6 dB / Pascal

6 dB / Pa * 6894.757 Pa /1 psi = 6 * 6894.757 * (dB / 1 Psi) = 41,368.542 dB / 1 psi

Note: This ratio should allow you to see that it takes a lot of dBs (sound pressure) to equal 1 psi (i.e. pressure evenly distributed over 1 square inch). That works out to be about 1 dB per 124.881645 square microns.

So, if dB is known & you want to convert to psi, then it can easily be computed as follows:

"120 dB = how many psi?"

120 dB * ( 1 psi / 41,368.542 dB = 120 / 41,368.542 = approximately 0.0029 psi

- Teacher

The conversion supplied by "teacher" above is only good for exactly 120db because of the logarithmic scale... The calcs using the logarythmic equation must be performed in si units and then converted afterward.

- Student

7 posts
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