The letter Q is often used to refer to VolumeAcceleration. VolumeAcceleration, or Q, can be thought of as the equivalent of an acoustic force. It has units of m3/s2.
For a mechanical system, Newton's Second Law of motion is F=ma. F is the force input into the system, a is the acceleration response output, and m is the mass. For an acoustic system, the Volume Acceleration (Q) is equivalent to the force in a mechanical system, and sound pressure (P) is the equivalent to the acceleration output response.
At first, it may not be intuitive how “VolumeAcceleration” is equivalent to acoustic force. The easiest way to visualize “VolumeAcceleration” is to think of it as Area (m2) multiplied by Acceleration (m/s2)
If one visualizes a speaker, imagine dividing the speaker surface areas into a series of small areas. In the center of each area, place an accelerometer. The total acoustic force that the speaker produces would be the sum of individual areas times their respective accelerations.
In practice, one must divide the surface into smaller and smaller areas as the desired frequency for analysis increases. In other words, the higher the frequency, the smaller the area patches. This is due to the change in the wavelength of sound.
What can Q be used for?
Utilizing a device called a Q-source, it is possible to take some interesting measurements.
Traditionally, when performing a measurement campaign to quantify the acoustic paths of a structure, one might employ an impact hammer (which measures force) and measure the acoustic response (sound pressure) with a microphone. This would result in a Frequency Response Function, or FRF, between the input location (perhaps a motor mount) and receiver location (a driver ear).
To quantify the sound contribution for a structure that had a motor attached to it at four locations, this could require 12 separate impact measurements: applying a force via an impact hammer at 4 separate mount locations in three different directions. The result is 12 separate Pressure/Force (P/F) transfer functions.
Using the Q-source, one could do these 12 measurements at a single time.
Putting the Q-source at the acoustic response location of interest, and accelerometers on the mount attachment locations, the measurement is performed at one time.
This is because P/F = A/Q, as shown below:
P = Sound Pressure in Pascals (Pa)
F = Force in Newtons (N)
A = Acceleration (m/s2)
Q = VolumeAcceleration (m3/s2)
P/F = N/m2/N = 1/m2
A/Q = m/s2/m3/s2 = 1/m2
Both P/F and A/Q reduce to the same units of 1/m2, making them equivalent.
Using a Q-source with LMS Test.Lab
To take a measurement with the Q-source, it can be attached to the source output of a SCADAS through a built-in stereo amplifier cable. The Q-source will produce a sound field. There is a BNC connector on the Q-source which outputs the Q signal.
For reference, click here for videos on Q-source setup.
In the "Channel setup" worksheet, select the following:
Much of the information to fill in comes from the Q-source calibration sheet.
The source can be setup as random in "Scope" worksheet of LMS Test.Lab Spectral Acquisition.
And select "FRF" as the measurement to save in the "Test Setup" worksheet of LMS Test.Lab Spectral Acquisition.
After performing the measurement, and viewing the FRF in a display, the FRF can be viewed as P/F rather than A/Q by right clicking on the Y-axis and selecting "Unit".
Comparison of Impact Measurements vs Q-Source measurements
Taking reciprocal FRF measurements with Q-Source yields equivalent results to impact hammer FRF measurements, but in less time.
See attached paper for more information on using a Q-source for Transfer Path Analysis.
Note: Even though the Q-source outputs Volume Acceleration, sometimes the sources are referred to as Volume Velocity sources.
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