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Calculating high-intensity acoustic sound pressure levels from piezoelectric microphone charge output sensitivity

Question

I am using the Endevco® model 2510 piezoelectric acoustic transducer to monitor the high-intensity sound pressure levels typically encountered during rocket launches. Given the piezoelectric operating characteristics of the transducer, would it also be possible to calculate sound pressure levels in decibels? If so, how is this achieved?

Answer

As a piezoelectric microphone, the Endevco® model 2510 acoustic transducer is a charge emitting device. As such, its charge output is measured in units of pico-Coulomb (pC). For reference purposes, we refer to the following formula for calculating pC units of measurement:

    • 1 pC = 1 x 10

-12

    • Coulomb

Where: 1 Coulomb = the amount of charge transported within 1 ampere-second

Acoustic sound pressure levels (SPL) are commonly measured in units of decibels (dB). They are usually referenced at the absolute threshold of hearing (ATH), or auditory threshold. ATH is an empirically derived number, reflecting the minimum level of a pure tone that an average human ear is capable of hearing. The term "sound pressure level decibels" (dB SPL) simply relates to the relationship between measured sound pressure and the "absolute threshold of hearing" (ATH).

ATH is denoted as the rms sound pressure of 20 µPa (micropascals), or 2 x 10-5 pascals (Pa) or 2.9 x 10-9 in English System. This unit of measure is also frequency dependent, usually ranging between 1 kHz and 5 kHz. The accepted unit for sound pressure level measurement is appropriately represented in logarithmic scale (dB SPL) because of its wide dynamic range.

The Endevco® model 2510 piezoelectric microphone was expressly designed for high-intensity sound pressure measurements ranging from 100 to >180 dB SPL, in temperatures up to +260°C.

Equation 1, below, shows the general formula for proper calculation of dB SPL within the English System. It is important to note that the charge output of the Endevco® model 2510 responds linearly with the level of acoustic pressure impinging on its diaphragm within its specified measurement range.

Equation 1:

    • dB SPL = 20 log P

i

    • / 2.9 x 10

-9

Where:

      • P

i

      • = Sound pressure in PSI

 

      • 2.9 x 10

-9

    • = Threshold of hearing in PSI

From the published performance specifications of the Endevco® model 2510, we know that the charge sensitivity (typical) value is 1069 pC/rms psi. This can be rewritten as shown in Equation 2, below:

Equation 2:

    • 1069 = pC

rms

    • /P

i

    • , P

i

    • = pC

rms

    • /1069

Where:

      • P

i

      • = sound pressure in units of PSI

 

      • pC

rms

    • = charge output sensitivity value

There are two accepted methods presented here for obtaining dB SPL values from the known charge output sensitivity of the model 2510. The first method is calculated using Equation 3, below. As an alternative, these values may also be represented graphically, as shown in Figure 1.

So, in the first method, we combine Equation 1 and Equation 2 into Equation 3, to determine dB SPL values as follows:

Combining of Equations 1 and 2:

    • dB SPL = 20 log (pC

rms

    • /1069)/2.9 x 10

-9

Equation 3:

    • dB SPL = 20 log pC

rms

    • /3.1 x 10

-6

As a quick application example: During a rocket launch where acoustic pressure levels are measured, we know that the Endevco® model 2510 microphone is outputting 15 pCrms. To accurately determine the acoustic sound level in dB SPL to which this output corresponds, using the formulas shown in Equation 3:

    • dB SPL = 20 log pC

rms

    • /3.1x10

-6

dB SPL = 20 log 15/3.1x10-6

The correct answer is:

dB SPL = 133.7

Or alternatively, we can utilize Method 2 to align graphical points, as show in Figure 1:


Figure 1: Graphical representation of dB SPL vs.
charge output values for Endevco® model 2510

For a more detailed description of this formula and its associated calculations, or for more information about the Endevco® model 2510 piezoelectric acoustic transducer, please refer to Technical Paper "TP278" on www.endevco.com, or click here to view the product page.