EE2.LabB: S4 Loudspeaker Frequency Response

Teams:	Two groups with 1-2 members
Software:	Audacity and Matlab
Timetable:	One week

Aims of the Experiment

To determine the frequency response of a loudspeaker, using recordings of the voltage and current, and sound pressure using a measurement microphone. To observe the resonant properties of the loudspeaker enclosure, and account for these in the loudspeaker response measurements.

Equipment

Loudspeaker drive unit and enclosure
Function generator
Audio amplifier
Oscilloscope
B&K 1/2" measurement microphone and B&K microphone preamplifier (shared)
Two Mac workstations with stereo audio I/O connections

Overview

The experiment measures the acoustic efficiency of a loudspeaker mounted in a box using an instrumentation microphone for various frequencies within the audio range. The acoustic efficiency is based on the ratio of acoustical power to the electrical power. Thus, one set of measurements determines the level of sound pressure produced for a given drive voltage; another set of measurements records the electrical current. In addition, we explore a number of different ways of making these measurements: using sinusoidal, swept sine (chirp) and white noise signals.

In part A, you use spot measurements with pure tones to record some manual data points at individual frequencies. Part B uses various test signals to examine a wider range of frequencies in a single measurement. Part C looks at the use of multiple measurements as a means of improving the accuracy of the estimated frequency response. Part D repeats the tests on another loudspeaker enclosure for comparison, which reveals the effect of different loudspeaker enclosures on the performance of the unit. Of the four parts, A and B are essential, C is strongly recommended and the last one D is optional.

Preparation

background reading on loudspeaker frequency response
revision of Matlab operation, such as via online tutorials
investigation into use of Audacity software

Hardware setup

For initial experiments feeding a sinusoidal signal into the loudspeaker, you will need the signal generator, audio amplifier and loudspeaker. The drive voltage should never exceed 1V peak, so be careful to check what you are doing as you connect these components. It is easy enough to burn the loudspeaker out, but it leads to rather disappointing results!
Now, you need to make one set of sound pressure measurements with the B&K instrumentation microphone, and one set of current readings just using a series resistor. However, we only have one B&K mic, so you will have to share with the other group.
Set the connections up as in figure 1, and check that you can observe both V₁ and V₂ on the oscilloscope, according to whichever configuration you plan to do first.
Using the aux input on the amplifier and one of the loudspeaker output channels, set the function generator up to give a sinusoidal input at 440Hz to the loudspeaker. A suitable voltage level should be chosen so that it is not too loud or overdriving the loudspeaker, but can still provide clean traces on the 'scope.

**Fig 1:** Loudspeaker measurement configurations for acoustic (config. 1) and electrical (config. 2) frequency response functions.

A. Making spot measurements of the frequency response

Microphone measurements (config. 1):

Set the 'scope display to give the amplitude and frequency (or period) of the sinusoidal voltage signals, the loudspeaker drive and the microphone signal (using the BNC output from the front of the microphone pre-amplifier).
Record the actual frequency, the magnitudes of the two signals, and relative phase between them (or equivalently the time difference) at the following points: 50Hz, 100Hz, 150Hz, 200Hz, 250Hz, 300Hz, 400Hz, 500Hz, 600Hz, 700Hz, 800Hz, 900Hz, 1kHz, 2kHz.

Current measurements (config. 2):

Set the 'scope display to give the amplitude and frequency (or period) of the sinusoidal voltage signals, the loudspeaker drive and the voltage across the 0.5Ω series resistance, which is designed to provide a measure of the current in the loudspeaker drive coil. Use a common point for the ground.
Record the actual frequency, the magnitudes of the two signals, and relative phase between them (or equivalently the time difference) at the following points: 50Hz, 100Hz, 200Hz, 400Hz, 600Hz, 800Hz, 1kHz.
Investigate the response in the lower part of this frequency range to find a point where there is a dramatic change in the magnitude and phase of the current. Record the details of this point.

B. Measuring several frequencies together

Put the 'scope and function generator away to one side, connect the audio output from one Mac workstation to the aux input of the audio amplifier, and connect V₁ and V₂ to the stereo audio input for the other workstation.
Using Audacity software and the sinusoid test signal below, make a 2-channel measurement for both of the configurations in figure 1 with a sampling rate of 16kHz. Having captured the responses with your recorded waveforms most likely with some surrounding silence, select just the section of interest and save is as a separate stereo WAV file.
Repeat the measurements for the chirp signal which sweeps from 100Hz up to 5kHz.
Repeat the measurements for the white noise signal.
Calculate the frequency response functions (FRFs) and plot the results, for which you can use and modify the Matlab script, calc_frf.m, which displays similar graphs to those in figure 2.

Test signals:
sinusoid chirp white noise

C. Improving the measurement accuracy

Select the test signal that gave you the most consistent (i.e., least variable) results across the required frequency range.
Make a total of eight FRF good quality recordings with your chosen test signal.
By finding a way to combine the results of these measurements in your calculation of the frequency response, show the results with 2 files combined.
Repeat this procedure for 4 files.
Finally, repeat this procedure for all 8 files.
Compare the quality of the results and, in particular, comment on the variance of the results as the number of files is increased.

**Fig 2:** Results for one set of loudspeaker measurements using a chirp signal, acoustic and electrical FRFs (upper) and acoustic efficiency (lower).

D. Comparing results for different boxes

Some example results are given in figure 2 for one of the loudspeaker boxes. Repeat your best frequency response measurements for the other two loudspeaker enclosures, if time permits, and compare the plots of your results. In particular, comment on the relationship between the low-frequency resonance and the volume of the box.

Dept.

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