# Determine Sound Intensity in SPL

I am recording ultrasonic sound using "Earthworks M50 50kHz Measurement Mic" and the sound card is "Rolando Quad-Capture USB 2.0 Audio Interface". The recording was done using Matlab into a wav file. Can anybody explain how can we determine the intensity of sound. What does the aptitude of a wav file represent? Is there any formula that we can use to find out SPL using the above information?

Since you have a measurement microphone, it should come with a manual that contains all necessary information to characterise it (if not with all this information in digital format too).

One crucial piece of information is its Sensitivity which is expressed in V/Pa (Volts per Pascal), at a specific frequency. This figure allows you to convert VOLTAGE (which is what you are measuring at the output of the mic) to PRESSURE (which is what the transducer responds to).

The sensitivity of the microphone, in combination with its frequency response will tell you how much VOLTAGE does the microphone produce for a reference PRESSURE level at a given frequency.

So, this mic states 36mV/Pa and is relatively flat from 10Hz to 10kHz. This means that a sound wave of Sound Pressure Level (SPL) of 1 Pascal falling on the mic's transducer will cause a 36mV signal to be generated at its output at any frequency between 10Hz and 10kHz.

Outside of these ranges, the curve is slightly lowered which means that the sound wave's SPL will still be 1Pa, but the output of the mic will not be 36mV but 36mV times the factor that is obtained from the frequency response.

So, now we have a way of converting between SOUND PRESSURE LEVEL (in Pascal) and VOLTAGE. What about what is hapenning in the sound card?

The sound card will have a pre-amplifier / amplifier to amplify the signal from the microphone and this amplifier will have a frequency response on its own which will modulate the frequency response of the mic. In other words, because of its construction, the amplifier will amplify different frequencies by slightly different factors, just as the microphone did.

To cut a long story short: A sound card's LINE level is 1.736V. The amplifier of the sound card is set to 1 and you are recording with 16bit resolution. This means that the positive peak of 1.736V is converted to the digital value of $2^{15}=32768$.

What value does 36mV produces? $\frac{36 \cdot 10^-3 V}{1.736 V} \cdot 32768 = 680$

Right, so when the WAV file reads a sample of 680 at an amplification level of 1, then we know that the microphone was producing 36mV and through its sensitivity we can infer that 1Pa of sound pressure level was falling on it.

So, to convert between your sample value and the sound pressure level that caused this sample value you need:

1. The microphone's sensitivity
2. The microphone's frequency response
3. The sound card's LINE IN Spec
4. The sound card's amplification level
5. The wordlength that was used during sampling.

Hope this helps.