UNITS CONTROL:

• User Units Toggle
• User Units Control Menu
  • Units Name
  • Unit/V Factor
• RMS Magnitude Spectrum Units
• Y-Axis Calibration Menu
  • Tilt:
    • +3 dB/Oct Pink Correction
    • +6 dB/Oct Step Correction
  • Calibration Files:
    • TXT2CAL Utility
    • Mic Cal On/Off
    • Load Mic Cal File
    • Spkr Cal On/Off
    • Load Spkr Cal File
  • Save Cal File - Calibrating Microphones
    • Calibrating Speakers
    • Xfer Cal Files (Transfer Functions)
  • Full-Scale (0 dB) Reference
  • Formulas For Working With Sound

USER UNITS (Units) TOGGLE:

You would use this option to convert from Volts to whatever units you are working with, such as mmHg for blood pressure or g for acceleration. You would also use it when you have an external preamplifier or attenuator before the input to the data acquisition board, to allow Daqarta to report the level of the original input signal even if it is still in Volts.

USER UNITS CONTROL MENU:

Units Name

Unit/V Factor

RMS MAGNITUDE SPECTRUM UNITS (U-RMS):

RMS inactive:

This mode is useful for directly determining spectral component amplitudes of a particular waveform. Each peak amplitude represents a sine wave of that same amplitude that is part of the overall signal. This representation is more common for mathematical analysis than for engineering work, where RMS measurements relate to equivalent energy.

RMS active:

Also, if you are combining several lines using the Root-Square method to get a total energy, it is logical to use RMS.

Y-AXIS CALIBRATION MENU:

Furthermore, they only affect the displayed data, not the raw, trace memory, or file data. This makes it easy to see the effects of a correction or calibration by simply toggling it on and off. You can change to a different calibration at a later time, such as if you find after an experiment that the system has changed and needs recalibration.

However, any currently active calibration or correction will be included if you save the data as a text file (OutTx), and a notation will appear in the file header indicating what was used. This is useful when preparing data for publication or off-line analysis.

TILT (+3 or +6 dB/Oct):

+3 dB/Oct (Pink Correction):

Pink noise has has a spectrum that falls at -3 dB per octave, which is more representative of real-world signals like music than the flat spectrum of a 'white' noise stimulus. Sound reproduction systems are thus generally designed to handle much more power at lower frequencies; if you used a flat stimulus spectrum you would need to run at very low overall power to avoid burning out the high frequency drivers, but then the low frequencies might be swamped by background sounds.

However, with a pink noise stimulus the 'perfect' system response would be a line that falls at -3 dB per octave, just like the stimulus. It is very difficult to judge how close a line comes to a particular slope, but it is trivial to compare it to the horizontal trace grid to tell if it is flat. Hence, the '+3 dB' Tilt option applies this correction for you.

This does not change your raw data in any way. The Tilt does not get saved with the data when you save to trace memory or to a file, with one exception: It is applied to text files, which you can use for publication or presentation.

+6 dB/Oct (Step Correction):

But the intended use is for quick system response measurements which might otherwise require a slow frequency sweep or a long noise average. The principle behind this is that the spectrum of an impulse response gives the frequency response of the system.

If you actually try that, you need a very narrow pulse, only one sample wide. You can experiment using the STIM3A Pulse Wave option. If you only want to view the raw pulse, and its spectrum, you can use the DEMO driver. But there is a simple trick you can do using the Square wave of the Virtual Source: Set the frequency very low, such that you see less than a half-cycle on the trace. There should be only a high-level line. Then adjust the trigger delay (and/or the slope) to get only the trailing edge of this high phase. Flip to FFT mode and you will see a perfectly flat spectrum, except for a big DC component.

However, there is not a lot of energy in this narrow pulse, and it may be hard for some types of sources to switch on and back off this quickly. A big voltage step, on the other hand, can have a lot of energy and is very easy to create. The derivative of a step function is an impulse function, so it is perfectly "legal" to apply a step to the system and take the derivative of the response to get the impulse response of the system.

The '+6 dB' setting allows a simpler approach, making use of the fact that a derivative applies a +6 dB per octave tilt to a spectrum. Here, we simply take the spectrum of the raw waveform, then apply the tilt to the spectrum. If the original spectrum was from a step response, the result will be as though it was from an impulse response. You thus see the frequency response of the whole system on every step.

But this trick has one drawback compared to a true derivative, and that is due to the nature of the FFT. Consider the step response of a low-pass filter: It rises up to a DC level and remains there for as long as the step lasts. But the FFT assumes that any set of input samples is just one cycle of a repeated waveform, as though the trace were "wrapped" from the right end to the left. In the case of the low-pass step response, the effective waveform would appear as a high-level baseline with large negative spikes... more like a distorted impulse reponse than a step response, and definitely not something we can use here.

Had we taken a true derivative of the step response first, the above problem would largely vanish. The derivative would give the true impulse response, and as long as that response was over by the end of the sample set, we could simply take an ordinary FFT. Of course, a true impulse response (or a step response) goes on forever, in theory. But once it has decayed below one bit of resolution, we can safely ignore the remainder. And in fact once we are familiar with a particular system we may not even need to let it decay this much.

So, for this "trick" method to work, you must make sure that the step response has pretty much decayed away before the end of the trace. That will never be true with low-pass systems, but it will be true for high-pass or bandpass responses... depending on the sample rate. You will need to slow the rate (or increase the number of samples) until you get the whole response on the trace. Then flip to the power spectrum and apply the +6 dB Tilt to see the frequency response.

One tip: Depending upon particulars of your test setup, you may need to adjust the trigger delay to eliminate any time lag before the actual response begins. You can usually tell that you need to do this because the raw waveform trace will show a flat portion before the sharp transient of the response. Just add anough trigger delay to elimiate that flat part.

Caution: Step and impulse tests work on the assumption that the system is linear throughout. This is NOT the case for many real-world systems, such as electromechanical and biological systems, if you push them hard enough. In addition to amplitude limitations like saturation or clipping, which can be troublesome even with conventional frequency sweep responses, some systems are susceptible to slew limit problems. This is where the system has some maximum rate of change that it can't exceed; if you drive it with a step or an impulse, it can't change fast enough to respond to the vertical edge, so it does the best it can and instead gives (typically) a constant slope:

        ___________
       |               Input Step
    ___|
            _______
          /
    ____/              Slew-limited Output

This is NOT the same as the exponential step response you might get from a linear system, and if you drive the system into slew limiting your resultant frequency response will not be the same as a conventional slow frequency sweep response.

This means that you should avoid or use extreme caution with step or impulse methods for most kinds of basic research, where you are exploring the response of an unknown system. These methods are best suited to monitoring known systems, such as in production testing of loudspeakers. When you are testing against a known response, even a certain amount of nonlinearity may be perfectly acceptable if you can still detect changes from the standard response.

As with Pink correction, Step correction does not affect the raw data, only the display, and is included in files only for text output (OutTx).

Calibration Files:

Likewise, you can supply a Spkr Cal file that describes the frequency response of a speaker or other output driver. This is intended for use in calibrating a "working" microphone from a given "reference" microphone, and for determining transfer functions of systems such as probe tubes.

Note that there is nothing in Daqarta that limits its use to sound transducers; 'Mic' and 'Spkr' can be thought of as 'Input' and 'Output', and you are free to use whatever type of transducers you want, with whatever units are appropriate for the transducer.

When a file has been loaded, the 'Cal File' header is replaced with the file name so you can tell which microphone or speaker curve is in effect. You may have as many files as needed, but only one of each type can be loaded at a time. However, either type (or both) may be replaced by an 'Xfer' type, which contains a unitless transfer function. So, for example, you could load a Mic Cal file as usual, then load the transfer function of a probe tube in place of the Spkr Cal file. (The 'Spkr' will change to 'Xfer'.) The combined effect will be to correct for that mic used with that probe tube.

Calibration correction is applied only to the display data and to text output (OutTx) files. The file name is also included in the text file header for later reference.

Calibration files may be created from text using the TXT2CAL utility, or from a measured response using the Save Cal File option.

TXT2CAL Utility:

If you can borrow a calibrated reference microphone, you can use it with its Mic Cal file to create a Spkr Cal file using the Save function, and use that to calibrate another mic to serve as your own reference.

Calibration data is usually provided as a response curve of mic sensitivity versus frequency. Sensitivity may be given in 'dB re: 1 V/Pa' or 'dB re: 1 V/µbar', or in millivolts per Pascal or per Newton/meter². There may be a graph with the flat part of the response shown at 0 dB, and a notation indicating that 0 dB is relative to some sensitivity of the above type.

As an example, consider a B&K model 4134 pressure-response condenser microphone. This has a typical sensitivity in the range of 10 mV/Pa, which is equivalent to -40 dB relative to 1 V/Pa. Since 1 Pascal (which is a Newton/meter²) equals 10 microbar, this is also equivalent to -60 dB re: 1 V/µbar. (See "Some Formulas For Working With Sound", and also the Glossary entry on dB.)

To use TXT2CAL, you first create a text file listing the response of the mic at various frequencies. It also gives the units and absolute sensitivity. Use any ordinary text editor for this, or a word processor with the file saved as 'text'.

An example file BK4134.TXT is supplied with Daqarta, and is reproduced here for reference:

    ;BK4134.TXT
    ;B&K model 4134 microphone calibration.

     SPL    ;Label for Y-axis (4 chars max)

    ;Mic sensitivity is -40 dB re: 1 V/Pa.
    134     ;94 dB SPL @ 1 Pa - (-40 dB re: 1 V/Pa)
    ;Start this line with 'k' if Freq values in kHz.
    ;Freq       dB
    0           -60       ;1st point MUST be 0 Hz.
    5           -4.1      ;Ascending Freq order.
    15          0         ;Any Freq spacing.
    8000        0         ;Any number of points.
    15000       1.0
    20000       0
    50000       -12.5

To create BK4134.CAL from this file, enter:

    TXT2CAL BK4134.TXT
 

You may place comments in the text file for your own reference. A comment begins with a semicolon; the rest of that line will be ignored.

The first active line should give the absolute units to be shown when using this file, usually SPL. This is simply a label for your own reference, which will appear at the head of the Y axis and in OutTx headers. There will always be a 'dB' added just ahead of whatever name you supply here, which may be up to 4 characters.

The second active line gives the sensitivity. Here you may need to do a little math, since the value is the SPL needed to produce 1 Volt (RMS) from the microphone. (If you use some other absolute units than SPL, it is the number of those units for 1 Volt output.) For most mics, the math is pretty easy once you know that 1 Pascal = 94 dB SPL.

For our example mic with a sensitivity of -40 dB re: 1 V/Pa, when we get a 1 Volt output we must be getting 40 dB more than 1 Pa, or 94 + 40 = 134 dB SPL. If you will be entering response curve data points (below) copied from a curve that has a 0 dB baseline, then enter 134 on this line.

Alternatively, if your entered curve uses the actual sensitivity values in dB relative to 1 V/Pa, enter 94 here. (But then be sure to enter the minus sign for each curve point, eg -40, etc.) If the values are in dB re: 1 V/µbar (eg -60, etc) , enter 74 here (94 - 20).

On the lines following this, give the frequency and response data points. Use a separate line for each frequency, and give the frequency in Hertz, followed by the response in dB on the same line. You MUST begin with the response at 0 Hz; make up something reasonable if you don't have that information. The 0 point is needed because TXT2CAL interpolates to create the actual file data, and this insures that it can interpolate as low as necessary.

If you wish to give frequency values in kHz instead of Hertz, add a line that begins with 'k' (without apostrophes). Place that line after the sensitivity line but before the first kHz value. If you want to give initial frequencies in Hertz and later ones in kHz, you can insert the 'k' line after the last Hertz line. The kHz mode stays in effect for the rest of the file.

You don't need any regular spacing between frequencies, but the points MUST be in ascending order. The simplest approach is to consider the response curve to be made up of straight line segments, and enter a point for the end of each segment. The sample file shows frequency and dB points separated by spaces, but you can use tabs or commas as well. You can even put everything on one line, as long as each frequency is followed by its proper dB value, but this makes it much harder to proof-read or modify.

One tip: TXT2CAL will create a .CAL file containing levels for 512 equally-spaced frequencies, including 0, up to the maximum frequency that you provide. When Daqarta uses this file, it will interpolate as needed to adjust the frequencies to match the current sample rate. If the sample rate is greater than twice the highest frequency in the file, then extrapolation is used... but that process is much less likely to agree with the true mic response. So the text file should include the highest frequency you expect to use, so that only interpolation will be needed.

On the other hand, there is no point to including frequencies considerably higher than you will use, since that only reduces the resolution (though not much, with 512 points in the curve). If your particular mic has a very irregular response, such as a probe tube mic, and you only expect to use it at low frequencies, then you can limit the curve to maximize resolution. You can create one low-frequency, high-resolution .CAL file, and another high-frequency, reduced-resolution file for other uses.

Also note that TXT2CAL requires the input text file to be less than 65536 bytes.

Mic Cal On/Off:

When Cal is active, the Y-axis header will change to 'dB SPL' or whatever units you entered in the text file for TXT2CAL. For example, if you had entered 'Pa', the header will change to 'dB:Pa', which is short for 'dB re: 1 Pa'.

The default full-scale reference at the top of the axis will change from 0 to 120 dB. Any changes you make with the FS Ref control or the SHIFT-Pg keys while Mic Cal is active will be stored separately, such that you can toggle Mic off and on and the full-scale value will change between the most recent settings in each state.

If PSD mode (SHIFT-P) is selected while Cal is active, the normal 'dB PSD' header will still appear. It will not show 'SPL', but it should be clear from the actual dB values that Cal is active since they will typically be positive values instead of negative.

Load Mic Cal File:

Besides Mic Cal files, you can also load Xfer Cal files to this location, but not Spkr Cal files... they must be loaded at the Spkr Load location below.

Spkr Cal On/Off:

A Spkr Cal file is typically used to calibrate a microphone. It holds the absolute output levels of a sound system at the location of the reference mic used during file creation. If you then remove the reference mic and replace it with an unknown mic, leaving the sound system unchanged, then with the Spkr Cal file active you can obtain the response of the unknown mic. That response can then be Saved as a new Mic Cal file.

When Spkr Cal is active, the Y-axis header will change to 'dB:V/Pa' if the original Mic Cal file header was 'SPL' or 'Pa'. This is short for 'dB re: 1V/Pa', meaning the reference for 0 dB is a mic sensitivity that produces 1 V output when 1 Pa of pressure is measured. (Normal mics will typically have values 30 to 40 dB below this.)

If the text file for creating the original Mic Cal used some other units, such as 'µbar', then the header will show those units in the same format, such as 'dB:V/µbar'.

Load Spkr Cal File:

Besides Spkr Cal files, you can also load Xfer Cal files to this location, but not Mic Cal files... they must be loaded at the Mic Load location above.

Save Cal File - Calibrating Microphones:

The basic approach is to obtain the frequency response of a system (mic, sound source, probe tube, etc) and while that response is displayed just hit Save.

Typically, you will first need a reference Mic Cal file that you create manually by using the TXT2CAL utility with data from a curve supplied with the mic. When that mic and file are in use, the trace will show the absolute sound level seen by the mic.

Next, you place the mic in a fixed position in a sound field, and use that setup to obtain the frequency response of the sound source. The best way to do this is with the STIM3A signal generator Sweep Step option, which was created for just this sort of application. Using the StepN mode, this can be set to step through all the lines of the spectrum one by one. If you then use Spectral Averaging in Peak mode, with Sweeps set to Continuous (by entering 0), you can capture the frequency response by hitting Pause after one or more complete scans of the spectrum.

This gives an "ideal" response that avoids some problems with a continuous sweep: As you may already know, unless an input frequency is exactly the same as one of the FFT spectral lines, energy will appear as "leakage skirts" at nearby lines. In that case, no single line on the trace will show the true amplitude of the input. But with a frequency sweep, things are even worse than simply getting a reduced response level: Since the input frequency is constantly changing, the amount of leakage is changing as well, so the final peak scan shows a ragged or "bouncy" response. Use of a window function reduces this problem; a Flat-Top window greatly reduces it, but doesn't cure it. The Sweep Step approach eliminates it completely.

The STIM3A Help system contains a detailed discussion of how to use the Sweep Step option this way. If is also possible to use the older STIM3 generator with a Key Macro that uses the Loop option to advance the frequency after each FFT, but it would be cumbersome.

There are other ways to get the frequency response of a sound system, such as by using a pulse or step response. You might also consider using white or pink broadband noise. These methods may be appropriate under certain circumstances, but they also have certain drawbacks. You will often need a considerable amount of averaging, and you still won't get as smooth a reponse as the Sweep Step approach. (Note that for the pulse or step responses you would use waveform averaging prior to toggling FFT mode, while for the noise responses you would use ordinary spectral averaging.)

Whatever method you choose, once you have the response of the sound system displayed, hit the Save control and you will be prompted for a file name to save it as. When the file is saved, the file type will be set automatically, based upon the current active calibration mode: If Mic is active, the saved file type will be Spkr, and vice-versa. If both are active (or neither) an Xfer file will be created. If an Xfer type is active in place of either Mic or Spkr, it has no effect upon the type saved. So with Mic plus Xfer active, for example, the Save type would be Spkr.

The Y-axis header used in the file will be based upon the active header at Save time. For instance, if Mic is active with a 'dB SPL' header, then the saved Spkr file header will (when later used alone) show 'dB:V/Pa', and if that file is then used to calibrate another mic, that saved Mic file will again result in the original 'dB SPL' header.

Once you've used Mic Cal to save a Spkr Cal file, you keep the entire physical setup exactly the same but replace the reference mic with the one you want to calibrate. It is very important that this be in EXACTLY the same location and orientation as the reference mic, exposed to exactly the same sound field.

Turn off the old Mic Cal, and load and activate the Spkr Cal file you just saved. Repeat the same Sweep Step peak scan (or other frequency response approach), and you will see the new microphone response. Then just Save that and you're done. If you have a lot of mics to calibrate, it only takes a few minutes per mic after the initial set-up and Spkr Cal procedure.

It's OK to use the same Spkr Cal file for all the mics you calibrate in a single session, as long as you keep the physical setup the same. But it's probably a good idea to create a new one for subsequent sessions, or even during the same session if you have to change anything.

If you will be doing a lot of mic calibrations, you should arrange some sort of fixture to hold each securely in place, maintaining the exact positioning from unit to unit.

The same basic calibration approach applies to free-field or coupler calibrations. You may be able to rig up a calibration coupler using a wide-range headphone in a sealed chamber, with a port to hold the desired type of microphone. (Commercial systems typically use a condenser microphone as a coupler driver, especially for calibrating other condenser mics. But besides being very expensive, such mics require high-voltage driving signals when they used this way.)

Allow your sound system to run for a few minutes before you create the Spkr Cal file, since some speakers change characteristics slightly as they warm up (woofers with butyl rubber surrounds, for example).

Be sure to set the sample rate at least as high as the highest you expect to use the mic with, so that you get the widest frequency response. Daqarta's calibration system interpolates between points, but extrapolation to higher frequencies is much less likely to give accurate results.

If you are using free-field calibration, you should give some thought to standing waves and room resonances. In theory, they shouldn't make any difference with this exact replacement approach. But in reality, the stronger the peaks and dips in the sound field, the more likely that something will change when you replace the reference mic with the unit being calibrated. You should try moving the reference mic around a bit and repeating the response scan before settling on a final position; if you get big response changes for small position changes, it's a warning that you may have problems later on.

You can try placing the mic relatively close to the speaker (a few inches away, in the "near field"), to reduce the room effects. A heavy blanket draped over the combined speaker / mic setup may also help to absorb room reflections. One problem with using conventional multi-way speakers (with separate woofers and tweeters, etc) this way is that when you move the mic close to the woofer, it's missing more of the tweeter sound.

Note, however, that it is not important to have a really flat sound field response at the microphone position, since the calibration system automatically corrects this. It's more important to reduce deep response notches than to worry about a gentle slope, even if it causes an ultimate drop of 20 dB or more relative to the main response.

Nonetheless, it is possible to use the drivers of a multi-way system individually, although it is a bit cumbersome. You first perform a separate calibration for one driver, creating a separate Spkr Cal file. When you get to the part where you are displaying the frequency response of the unknown mic, you save it as a text file with OutTx (ALT-O) instead of the normal Save Cal File control. Then move the setup to the next driver and again use the reference mic to create another Spkr Cal file, and use that with the unknown mic to create another text file.

While you are doing the above, you should pay attention to the best frequency range of each driver, usually where you get the biggest response. If you already know the ranges, you don't really need to run the Sweep Step over the rest of the spectrum.

Now use a text editor and manually combine the text files to create a single file using only the best range of each driver. You will need to remove or comment out (with a semicolon) the normal OutTx header information, and add some items for the TXT2CAL utility. You will probably want to use 'SPL' for the header, and 94 dB for the reference value. Since OutTx typically shows frequencies in kHz instead of Hz, you will also need a line that starts with 'k' before the first frequency in the list. TXT2CAL will interpret all frequencies after that as kHz, and create a composite Mic Cal file.

Calibrating Speakers:

But there is a catch: You can't measure the response of the output unless you know the response of the input, and sound cards like early Sound Blaster 16 models had poor low-end input response. So you may want to check that first. See 'Measuring Input Frequency Response' in the SB16 Help system for a way to avoid this chicken-and-egg problem by using a pulse generated by the printer port.

If you find that you can't create a flat output response for speaker calibration, you may be able to correct it using the Xfer Cal option.

When you are driving the speaker with 1 VRMS at all the needed frequencies, set up your calibrated mic at 1 meter and run a response curve with Mic Cal active, just as if you were going to create a Spkr Cal file as described above. This response will be shown in SPL, and since you've set 1 Volt and 1 meter, it's just what you need. You can save it as a text file using OutTx; just remember that the labels will only say 'SPL', and you will have to remember (or add manually with a text editor) that this is 1 Volt at 1 meter.

Xfer Cal Files (Transfer Functions):

A microphone calibration curve is a special kind of transfer function for a 'transducer', which converts energy from one form (sound pressure) to another (electrical voltage). A microphone transfer function is thus typically expressed as the output in Volts for a constant sound pressure in Pascals, as 'dB re: 1V/Pa', which Daqarta abbreviates to 'dB:V/Pa'.

You can use the Mic Cal (and Spkr Cal) files with other types of transducers, just by supplying the appropriate units in the original text file for TXT2CAL. Daqarta assumes that this file is for a transducer that converts an input into Volts (since that is what the ADC input actually sees), but it doesn't matter what the original units are: You could just as well use acceleration, velocity, position, or photons, for example. You can then calibrate other input transducers of the same type through use of an intermediate Spkr Cal file, which is assumed to have been created using the given input transducer and Cal file with an appropriate output driver.

But unlike transducers, many systems keep the same type of energy from input to output. For example, an electrical filter may be used to reduce an unwanted range of frequencies in its electrical transfer function, or a probe tube for a microphone may have unavoidable dips and peaks in its acoustical transfer function. Since the units are the same on input and output, the proper axis label is simply 'dB' to show a relative change.

Suppose you have a collection of different probe tubes for use with one or more microphones. Each tube has its own response, which must be considered along with the response of the mic when making any measurement. You would set Mic Cal with the proper microphone file, and replace the Spkr Cal with an Xfer Cal file for the probe tube. Then the display would show the true sound level at the entrance to the probe tube, instead of at the membrane of the microphone.

To create the Xfer Cal file, use the same setup as for doing microphone calibrations, as discussed under Save Cal File. After creating a Spkr Cal file for the sound setup, you load that and activate it along with Mic Cal. You should get a perfectly flat response from this combination, since you used that mic to create the Spkr file in the first place. Now add the probe tube to the mic, and the new response will show only the effect of the probe tube, independent of the speaker or mic. Hit Save and (since both Mic and Spkr are active) this will be saved as an Xfer Cal file type.

Now if you want to use the probe to make measurements, load that file in place of the Spkr Cal file and activate it along with Mic Cal.

Full-Scale Reference:

This control allows use of a sensitive log range that only shows a narrow portion of the total signal range, but can be "slid" up or down for a magnified view of any details.

You don't have to use the menu control; the SHIFT-Pg keys allow you to scroll the value directly.

The default setting here is 0 dB, but whenever Mic Cal is active a separate setting is used with a default of +120 dB. The two settings are completely independent. This allows you to look at large positive dB SPL values when Mic Cal is active, and negative dB values (relative to 0 dB full scale) otherwise. There are similar independent settings for Spkr Cal, and for the condition when both Mic and Spkr are active.

Note that you can use SHIFT-HOME to go to a preset log range and full-scale reference, and return via SHIFT-END.

   SOME FORMULAS FOR WORKING WITH SOUND:

     1 Pascal (Pa)  =  1 Newton/m²

                    =  10 dyne/cm²

                    =  10 µbar

                    =  94 dB SPL

       Sound Power Level (SPL):               ³

       SPL = 20 * log(P / P0)

 where P is the measured pressure and P0 is
 a reference pressure in the same system of
 units:

     P0  =  20 µPa  (or µNewton/m²)

         =  0.0002 µbar (or dyne/cm²)

 This reference pressure corresponds to a
 sound wave in free air with an intensity
 (power) I0 = 10^-16 Watts/m², which is used
 as the reference for intensity in dB:

     Intensity = 10 * log (I / I0)

• Back to Units Control contents.
• Daqarta for DOS Help Contents.
• Daqarta for DOS Help Index.
• Daqarta home page.
• Daqarta download options.
• Free Daqarta for DOS Registration

Questions? Comments? Contact us!