“If you saw a heat wave, would you wave back?”
– Steven Wright
Part 1: The Myth(?)
Once upon a time, back in the “olden days” (as my kids call them), before I worked at Bang & Olufsen, I did a Master’s degree at McGill University as a tonmeister (hence the domain name…). In practice, this means that I was trained to be someone who knew as much about things like room acoustics, microphone techniques, recording practices and electronics as I did about music. (Of course, if I knew nothing about music, then this equation falls apart…) In practice, what it meant was that I spent a LOT of time in recording studios (literally more time than I remember) doing recordings or just listening to them.
Now, let’s think about the design of a typical “good” recording studio control room. Usually, you have a mixing console in the middle of the room, and at least one pair of small studio monitor loudspeakers sitting on the meter bridge. Also, up on the front wall, there’s a large pair of “soffit mounted” loudspeakers built into it. Figure 1, below, shows an example of this.
One story I heard back in the “olden days” was that, if you’re building a recording studio, you should always keep the amplifiers for your big soffit-mounted loudspeakers away from (or at least above) the loudspeakers themselves. You should never NEVER put the amps directly under the loudspeakers. The story went that the reason for this was that hot air rising from the amplifiers would waft past the tweeters, modulating (changing) the speed of sound of the air between the tweeters and the listening position. And, since this modulation was random, then this heat would sometimes cause the right channel to arrive at the listening position earlier than the left, sometimes later. The result (according to the story) would be a constant shifting of the phantom image, moving left and right instead of staying exactly in the middle where it should be. The analogy/metaphor/explanation was that the image location would “shimmer” in the same way that there appears to be water on hot asphalt in the distance on a summer day, or the way you can see heat rising from a hot surface like a barbecue.
Fast-forward about 25 years, and I’m sitting in a meeting at B&O, discussing mechanical design options for high-end loudspeakers. Someone in the room says “one possibility is to put the radiators for the amplifiers on the face of the loudspeaker, just under the midranges and tweeters” and I say “you can’t do that – you’ll screw up the phantom imaging”. Heads turn to look at me, the expressions on the faces obviously say “what on earth are you talking about?” So, I tell the story that I heard back in the olden days…
Quick sidebar: if you don’t already know, almost all Bang & Olufsen loudspeakers are active loudspeakers, which means that the amplifiers and power supply are inside the loudspeaker enclosure. Amplifiers and power supplies are never 100% efficient. In addition to this, because we use DSP to control the loudspeaker, we can push our loudspeaker drivers to their limits without melting their voice coils – this also results in a lot of heat. All of this means that our loudspeakers need a lot of thought into their thermal design – basically, we need to make sure that the heat can get out, which is why we need radiators like the one shown in the photo on the right (which shows the bottom of the back of a BeoLab 20. The vertical stripes are a metal radiator attached to the electronics inside.). We now return you to your regularly scheduled story…
Some of the engineers in the room say “that’s crazy” – and others (the ones I like) say “let’s find out…” So, using the modern tools for finding-things-out, we started by typing things like “loudspeaker amplifier heat phantom image” into Google. This resulted in no information – or at least no useful information. So this meant that we had to do an experiment.
Part 2: The pilot experiment
Okay, so the question is: does heat rising in front of a tweeter have an effect on the sound that it radiates? And, if so, what is/are the effect(s) and what kind of magnitude of effect are we talking about? The easiest way to find this out is to exaggerate the effect. So, we got a tweeter and a hot plate (which lives in the acoustic department exclusively for warming risalamande at the yearly Julefrokost (the ubiquitous Danish “Christmas lunch” literally translated, although it can happen as early as November, it rarely starts at lunchtime, and typically extends well into the evening…) and we set them up as shown in Figure 2.
We put a microphone in front of the tweeter at a distance far enough away that the microphone wasn’t getting heated by the hot plate (about a metre or so…), and we sent a high frequency tone (20 kHz) to the tweeter from a sine wave generator. Then we simply sent the original signal and the output of the microphone to an oscilloscope so that we could look at them in real time.
Figure 3 shows the result when the hot plate was turned off. The original signal and the microphone signal are both clean, as you can see there.
Figure 4 shows the same thing, but the hot plate is now set to “medium”. As you can see there, the output from the tweeter is much more “blurry”. This is because it is moving on the screen over the 30 seconds of the photo exposure. Note that it is moving in both the X-axis (meaning the level was changing over time) and the Y-axis (meaning that the time of travel from the loudspeaker to the microphone was changing over time).
Figure 5 shows the same thing, but the hot plate is now set to “maximum” (hot enough to boil water or to burn risalamande). As you can see there, the output from the tweeter is even more “blurry”for the same reason. It’s also fairly easy to see in that photo that the output from the tweeter is modulating in both axes.
One thing to be clear of here is that we are looking at the effect of modulating the temperature of the air in front of the tweeter. We’re not changing the temperature of the tweeter itself (at least, not with the hot plate – the tweeter heats itself, but that’s another story) or the microphone.
Part 3: The “real” experiment
Okay, so we had some proof that the story that I heard back in the recording studio might be true. At the very least, we found out that it would be easy to measure the effect of heat rising in front of a tweeter. Now we had to get a little more useful data by analysing the signal from the microphone a little better. Looking at the signal on an oscilloscope is good for intuition, but it’s hard to graph the results.
So, this time we changed the setup a little. We used a little studio monitor loudspeaker (with some minor alterations – we taped over the ports to ensure that we weren’t modulating the air around the loudspeaker as a result of airflow through the port, just in case… for the lower frequencies… Since we were only playing sine tones and we’re not really interested in the absolute magnitude response of the loudspeaker, the lack of a port didn’t matter too much to us…) and we recorded the microphone output instead of just looking at the signal on a ‘scope. (We were also careful not to move during the recordings, partly to reduce background noise, but also to avoid creating air currents … just in case…) The total setup (although it’s still pretty simple) is shown in Figure 6.
We also tried measuring the air temperature in front of the loudspeaker, but this was difficult because it was fluctuating so much and so rapidly. So, instead, we put a power meter on the mains feed to the hot plate to get a better idea of how much constant power we were using.
Our analysis was to see how much the phase and the magnitude were changing over time with different frequencies and different settings of the hot plate temperature. This was done by analysing the recordings of the microphone signal for a 30-second period. The results turned out to be different for different frequencies – and surprisingly large in some cases…
Some details for the geeks-amongst-you:
- The recordings were done with a 192 kHz sampling rate so that we had plenty of bandwidth to play with for the next step.
- We took each 30-second recording and band-limited it to a frequency band 2 octaves wide using second-order high pass and low pass filters, with the tone being the centre frequency (geometrically). (In other words, for example, the 16 kHz recording was band-limited from 8 kHz to 32 kHz). The reason for this was to reduce the influence of background noise in the recordings for the level analysis.
- The phase analysis was done based on the output of a single FFT bin which provided its own noise immunity.
- The recordings were done at 5 power consumption settings of the hot plate: 0 W, 75 W, 150 W, 300 W and 700 W. These roughly corresponded to air temperatures in front of the tweeter 25º C, 28º C, 30º C, 34º C, and 44º C. I say “roughly” because the air temperature in front of the tweeter was varying quickly and widely, so this is just a ballpark measurement to get a rough idea of the effect of the hot plate. Due to this uncertainty, the plots below are relative to the power consumption of the hot plate rather than the air temperature.
As you can see above in Figures 8a and 8b, there was almost no effect on a 250 Hz tone, even when we pushed the hot plate up to 700 Watts. There is a very small change in magnitude, however this might be caused by background noise.
As you can see above in Figures 9a and 9b, at 1 kHz the effect is not getting much more noticeable.
Figures 10a and 10b, show the modulation for 4 kHz. Now we’re starting to see some effects…
Figures 11a and 11b, show the modulation for 16 kHz . You can see there that, in a worst-case scenario, we’re getting magnitude changes on the order of +/- 3 dB or so (which would mean, in a stereo system, a worst-case difference between the two loudspeakers’ signals of about 6 dB), and phase changes on the order of about +/- 40 degrees (so a worst-case difference between the two loudspeakers’ signals of about 80 degrees).
If we then look at the peak-to-peak variation in the above graphs and plot that as a function of hot plate power consumption for the different frequencies, we get the results shown in Figures 12 and 13.
So, the conclusion from the measurements was that the effect was considerable at high frequencies and high temperatures, but might be significant at lower values as well… the question was to ask “what is significant?”
Luckily, for the phase modulation part of the question, we had a partial answer from an experiment that we did a long time ago. In a paper called “Audibility of Phase Response Differences in a Stereo Playback System. Part 2: Narrow-Band Stimuli in Headphones and Loudspeakers” (Presented at the 125th) , Sylvain Choisel and I reported that subjects were able to detect phase response differences in loudspeakers with a threshold of approximately 50 degrees phase difference, regardless of frequency – although we only tested up to 8 kHz… Apart from the 16 kHz measurements in this experiment, none of the frequencies we measured came close to a worst-case difference of 50 degrees – so we’re probably safe on that one. (Although geeks might be interested to see the below for a little more discussion about this issue looking at it from a perspective of time instead of phase.)
The magnitude response differences may be a similar story. Many studies have been done to find out what differences in level between loudspeakers result in changes in phantom image placement – for example, see this site for a good summary. As can be seen in that graph, a 1.5 dB difference (chosen because that’s the worse-case value for the 1 kHz curve in the plot in Figure 12) in level between the two loudspeakers (measured at the listening position) will result in something like a 15% to 20% shift in phantom image location away from centre (that’s 15% to 20% of the distance to one of the loudspeakers from centre) which will probably be noticeable if you’re paying attention, although it might sound more like a “fuzzy” centre image instead of a moving one… A 6 dB difference (roughly the worst-case value for the 16 kHz curve) can result in an approximately 60% shift in phantom image location. Note, however that we might be jumping to (incorrect) conclusions here, since some of the data in the plots on that PDF file I linked to above are from listening tests with full-range signals. Whether the values will be valid for narrow-band signals, especially at 16 kHz is unknown…
Part 4: Phase vs. Time
Take a look at the side view of our setup, shown below in Figure 14.
This is a simplified version of what is happening in the experiment. The sound wave travels outwards from the tweeter, through the air. However, that air has one area where the temperature is significantly different than the rest of the room.
The speed of sound in air can be calculated as follows:
c = 331.3 + (0.6 * T) m/s
where T is the air temperature in degrees Celsius.
So, for example, if the temperature of the air increases by 10ºC, then the speed of sound increases by 6 m/s. If the temperature increases by 50ºC, then the speed of sound increases by 30 m/s. This will change the time of arrival of the sound at the microphone – the hotter the air, the earlier the sound arrives.
However, this change is a change in time. This converts to a change in phase in the sine wave that we were measuring – but you have to remember that a given change in time is equivalent to a change in phase that increases with frequency. For example, a 1 ms delay change is equivalent to a 45º phase shift at 125 Hz, but a 90º phase shift at 250 Hz, a 180º phase shift at 500 Hz, and a 360º phase shift at 1 kHz, and so on…
So, another way to look at this problem is to consider the change in interchannel delay instead of interchannel phase. If you take a look at this site again, you can see that our perception of the phantom image location in a stereo system is very sensitive to changes in interchannel delay. For example, according to Simonsen, an interchannel delay difference of only 200 µs (that’s 0.0002 seconds!) will result in a 30% change in phantom image location. In other words, if you have a “correct” stereo configuration where your loudspeakers are placed +/- 30º from centre front, then delaying one loudspeaker by 200 µs will move the centre phantom image to 9º off-centre (or 30% of the way to the earlier loudspeaker).
Let’s simplify, just to get an idea of what we’re talking about in our experimental results:
Case 1: If the microphone is 3 m from the tweeter and the air temperature is 25º C for all 3 m of travel, then the speed of sound for the entire trip is 346.3000 m/s and the total travel time is therefore 8.6630 ms.
Case 2: If the microphone is 3 m from the tweeter and the air temperature for the first 50 cm of travel is 44º C and the remaining 2.5 m of travel is 25º C, then the speed of sound for the first 50 cm is 357.7 m/s and for the remaining 2.5 m it’s 346.3 m/s. This means you have a total travel time of 8.6170 ms.
The difference between Case 1 and Case 2 is 8.6630 – 8.6170 = 0.046 ms or 46 µs, which, according to Simonsen’s results would correspond to something like a 5% shift in centre image location. Audible? Perhaps, but just barely… However, if you’re checking my math, you’ll note that a 46 µs change in time is equivalent to a 264º change in phase at 16 kHz, which was much larger than the roughly 85º we measured in the analysis above (see Figure 13)… So, my simplified example here seems to be exaggerating the effect, which means that a guess (even a calculated guess) of a 46 µs interchannel latency difference is probably an overestimate…
So, we might be able to conclude that the effect of this with respect to change in time of arrival are also inaudible, according to the data…
Part 5: Why is the level changing over time?
You may notice that I’ve avoided an obvious question throughout the above: “Why does the magnitude of the signal change?” If you look at this site, for example, you’ll see that although there is a change in sound absorption with change in air temperature, it is a very small effect. So, why do we measure such a large change in magnitude (or level) correlated with the temperature of the hot plate? There are two possible explanations for this.
The first was already discussed. At low temperature settings, the variation in level is probably simply an artefact of the background noise. All of these measurements were done in the Cube at B&O – which is normally used for a different kind of measurement which is more immune to background noises. This means that the Cube itself doesn’t have to be quiet, so it isn’t soundproofed from the outside world. Extraneous noises such as wind, rain, or someone walking by pushing a cart in the hallway, are easily audible if you’re sitting in the Cube. However, for the measurements in this experiment, those background noises will infect the results.
The second explanation is not related to background noise. As you can see in Figure 12, at higher frequencies, there is a definite increase in level variations caused by increasing temperature of the hot plate. However, the effect is too big to be attributed to absorption changes related to temperature changes. So, what is it? Our best guess is that it’s the result of the changes in thermal currents (in other words, the hot air rising) in front of the tweeter resulting in thermal gradients (differences of temperature in space). This causes differences in speed of sound in space causing refraction of the wavefront. The higher the frequency, the more the tweeter is “beaming” so the effect is more evident than it is at low frequencies where the loudspeaker is more omnidirectional. (Spinning a flashlight generates a more obvious than spinning a naked light bulb.) As the temperature changes in time, the sound beam from the tweeter moves towards and away from the microphone input, which looks like a change in level.
If we had used a cluster of microphones instead, we would very probably have seen the “beam” moving to another microphone as it went quiet at the main mic… Maybe we’ll do that experiment someday and call it “research” – but for now we have the answer we were looking for, so we’ll leave that one for another day…
So, after all that, our end conclusion was, for an active high-end loudspeaker, we should not put radiators directly below the midranges and tweeters – it’s better to put them behind the loudspeaker like we do already in the BeoLab 5 or BeoLab 20, for example. Or perhaps above the tweeter could also be an option – although that might be a challenge for the visual designers…
There’s no guarantee that the artefacts will be audible (in fact, they almost certainly won’t if you’re not paying attention to the phantom image location, or if you aren’t sitting in the sweet spot… but if those were the case, we probably wouldn’t be talking about a high-end loudspeaker…) but the artefacts are certainly measurable – and that’s enough for us to go looking for a better place to put the amplifier radiators.
And now, I guess this also means that when someone types “loudspeaker amplifier heat phantom image” into Google, they’ll get an answer…