Interpreting My Measurements

Measurements are an important part of any speaker review. They give us something to talk about besides my own subjective opinions of sound quality. They help to verify with some degree of confidence that my ears aren’t lying to me, and they allow a quantification of speaker performance. Of course, they are also very hard to do. Not only do you need the appropriate gear, you need the appropriate software and appropriate room to do it all correctly. Right now, I have none of those things. I do have a good microphone, and a room which is acoustically “not horrible”. There are bookshelves in three corners,  a desk in the other, curtains on three walls and an open door on the other. The ceiling has a fan and the floor is carpeted. The loudest reflections and standing waves are pretty mitigated here.  There are plenty of room nulls as you will see, but they do not distract from understanding the sound of a particular speaker at the level of nuance we deal with here. However, in order to make sure the direct path from the speaker dominates by enough, I keep the microphone 2 meters away from the speaker.  Software, on the other hand, is something I can take care of. By education and profession, designing the types of software a procedures to generate these kinds of measurements is second nature to me. If some of that went over your head don’t worry, I’m just trying to say I’m doing the best I can with a difficult problem.

Logarithmic Scalings

When dealing with sound, two quantities are often expressed on logarithmic scales, frequency and amplitude. With frequency, the explanation is pretty simple. When we talk about about frequency in the context of music, it is interchangeable with the tone of a note. Every dot on a musical scale is telling you “play this frequency for this long”. Now, when dealing with notes, the distance between each semitone is not constant. So while one octave may go from 220Hz to 440Hz, the next one goes from 440Hz to 880Hz. If we choose to display frequency so that each octave takes up the same amount of space on an axis, it is equivalent to spacing the frequencies by their logarithm, rather than their actual value. This means that the area given to frequencies between 100Hz and 1000Hz takes up just as much space as frequencies between 1000Hz and 10,000 Hz. Likewise, amplitude measurements are done in decibels, simply because the values are so loud, measuring them by the number of zeros behind the sound pressure is more useful than the actual value.

Chirp Response

The first test I run with each speaker is to play a chirp signal. A chirp signal starts at one frequency and continuously moves towards another. I’ve done my chirp signals so they advance logarithmically in frequency, they spend an equal amount of time in every octave. Since I know what the sound wave looks like at any given time from my microphone, and I know what frequency is being played at any given time, I can estimate how loud the speaker is playing any arbitrary frequency. That’s exactly what the blue curve in the below graph is, my estimate of how loud a sound the speaker is making if I put out a constant level at different frequencies.

Pink Noise Response

Pink Noise is a term for noise which has equal energy in every octave, and every fraction of an octave at all times. So rather than go and play a single frequency at a time and figure out how loud it is, we record every frequency at all times, then look and see how much energy was in each band (in my measurements 1/12th of an octave, aka one for each musical note). Both this and the chirp response are valid ways of measuring a speaker’s characteristics. Its obvious how close the measurements between the two cases are. The reason to use both is they are two different ways of arriving at the same answer, if they disagree, finding out why is important to know. Looking at the response below, there is a large outlier at 56Hz from the pink noise and not the chirp. This is from my room heater, and it shows one of the weaknesses of the pink noise response, constant background noise increases the output of the filters. Conversely, transients affect the chirp response while the pink noise response is robust to them. That’s why you do them both.

b652-air

Chirp Image

The best way to understand how a signal changes with time is through a spectrogram. It takes segments of time in the signal and looks at what is going on in frequency. Its then plotted as an image where changes in the frequency content of the signal can be easily observed with time. While not a standard test for speaker measurements, its interesting to look at and see what can be found. The diagonal line running through the image is the chirp signal. It’s ups and downs follow the blue curve above. The horizontal patterns represent things happening throughout the test, in this case, my heating system. The thin diagonal line above the chirp is distortion, in this case third harmonic. My suspicion is this is an artifact from the amplifier during the crossover.

b652-air-image

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