The main purpose of specifications is to allow us to make sure that we have the right tool for the job. But what does this information really mean?
March 30, 2012, by Pat Brown
For the majority of humans, there is nothing simpler than listening to sound. You simply, well, listen.
When it becomes necessary to describe the listening experience analytically, however, a host of complex equations and diagrams are required to describe even the simplest of sonic events.
The benefit of mathematical analysis is that it can yield insights that are not apparent through intuition alone.
Acoustic signals are easily measured, and the audio components that produce them have characteristics that can be measured.
We do not expect specifications to tell us how a product sounds. This is what listening is for.
The main purpose of specifications is to allow us to make sure that we have the right tool for the job, and this information is most often presented in the form of charts and graphs.
But what does this information really mean?
The heart of understanding the specification sheets that describe audio products is the understanding of dependent and independent variables.
The concept is one that most people use every day, though often without realization.
An independent variable is one that describes a series that has a fixed value.
For example, the time of day in the city that you live in is an independent variable. Regardless of what happens tomorrow, time will progress like it did today.
What will change are your moment-to-moment activities. These events represent a dependent variable. They depend on time.
If you look at a page in your day planner, you are looking at a plot of activities vs. time.
Time is the independent variable. It is the same on every page of the planner.
The scheduled events are the dependent variables, because where you go and what you do depends on what time it is. Most graphs show the relationship between dependent and independent variables.
Now let’s look at a variation on the theme. Let time be the independent variable (it usually is) and let the loudness of the sound system during a show be the dependent variable.
The plot might look something like Figure 1.
Figure 1: In this example, time is the independent variable while loudness is the dependent variable (click to enlarge)
The horizontal axis represents time (the independent variable) and the vertical axis represents loudness (the dependent variable).
We will call the horizontal axis the x-axis and the vertical axis the y-axis, although any two letters would do.
The values on each axis are usually discrete, meaning that they are individual samples, points, or measured values called data points.
The fact that most graphs look like squiggly lines just means that after many data points were taken, they were joined with a line to make it easier to read.
Such two-dimensional plots are found on virtually every good specification sheet in existence. They simply answer the question “What is the value of y when the value of x is this?” Some examples of two-dimensional plots found in audio engineering include:
Each plot shows the value of y for a given value of x. Pretty cool. In math-speak, in each case it can be said that y is a function of x. (We sound smarter when we say it like this.)
From this example, it can be seen that frequency is a very common independent variable in the world of audio and acoustics. The y parameters are said to be frequency-dependent.
In audio and acoustics, almost all parameters that we care to know anything about are frequency-dependent. This means that the answer to virtually any question regarding any of the y parameters is “it depends.” Y depends on x.
An example of a frequency-dependent parameter is the setting of a graphic equalizer. In fact, it’s a really good example because it is basically an xy plot of the type that we have been describing.
The x variable is frequency, and the y variable is relative level. The y value depends on the x value.
When you look at the front panel of a graphic equalizer, you are looking at an xy graph, which is why it’s called a graphic equalizer.
What Time Is It?
Another common independent variable is time. Many parameters in audio and acoustics are time-dependent. Examples include loudness, temperature and background noise, just to name a few.
Note that Figure 1 just gives us values. It’s still up to us to know what they mean and how to apply them.
Graphs are valuable because they give us some visual feedback regarding trends in the data. For instance, a glance at Figure 3 (later in this article) shows that the loudspeaker’s on-axis directivity is increasing as a function of frequency.
This means that everyone in the room might hear the low-frequency events, like a bass guitar, but only those in front of the loudspeaker will hear the high-frequency events, like the crash of a cymbal.
It’s clear why we would want the directivity of a sound reinforcement loudspeaker to be “frequency-independent.” The directivity of such a device would be a straight horizontal line.
It’s also important to consider the resolution of the graphed data. The closer together we place the points on the x-axis, the less likely it will be that we missed a significant data point when we measured.
For example, we could take the page of a day planner and break the time axis down into hours, minutes, seconds, or even fractions of a second.
Obviously, there is a point of diminishing return on resolution. It must always be appropriate for the data being plotted.
If you were plotting the arrival time of the tweeter in the main array to the back of the balcony, then one millisecond resolution would be meaningful.
But that same resolution would be extreme overkill for plotting your daily schedule.
What time resolution do I need? Again, it depends!
Following are some examples of common plots found on data sheets, with plain English descriptions of what each one means.
After digesting each, download some data sheets from various manufacturers and attempt to interpret them.
Use them to form an understanding of the product, what it does, and how it might compare to a similar product.
Remember that to fully describe the performance of a product, and infinite number of graphs would be required.
Most “one-number” ratings in audio and acoustics have little meaning.
They usually over-simplify something that is much too complex to specify with a single number.
Unfortunately, many people base their gear-buying decisions on this meaningless data, and then wonder why the gear does not live up to their expectations.
A graph is much better, but even graphs can’t tell the whole story.
We live in an amazingly complex world!
Figure 2: The frequency response plot answers the question “What is the relative on-axis level change of the device-under-test regarding frequency?” (click to enlarge)
What’s The Frequency?
In Figure 2, the independent variable is frequency. The dependent variable is level. The frequency response plot answers the question “What is the relative on-axis level change of the device-under-test regarding frequency?”
For a device that produces the same level at every frequency, the plot would be a straight, horizontal line.
A real-world loudspeaker response is also shown. Some would consider a flat line response to be the best possible loudspeaker; however, a spectrum plot alone does not tell the whole story.
Now, let’s return to Figure 3.
Figure 3: At a glance, we can see that the loudspeaker’s on-axis directivity is increasing as a function of frequency (click to enlarge)
Again, the independent variable is frequency, while the dependent variable is the on-axis directivity.
The directivity plot answers the question “What is the ratio between the sound intensity on-axis to the total radiated sound intensity as a function of frequency?”
Q = 1 means that the device is omni-directional, where Q = 10 means that the intensity on-axis is 10 times the average radiated intensity.
Q = 100 means that the axial intensity is 100 times the average intensity.
Another way of describing the same thing is to use the directivity index, which is the Q rating converted into decibels with the formula DI = 10logQ.
It yields the same information in decibels, giving the loudness advantage produced by controlling the sound radiation.
DI and Q are often found on the same plot.
Turning our attention to Figure 4, once again the independent variable is frequency.
Figure 4: The impedance plot shows the opposition produced by the loudspeaker to current flowing from the amplifier as a function of frequency (click to enlarge)
The dependent variable is impedance.
The impedance plot shows the opposition produced by the loudspeaker to current flowing from the amplifier as a function of frequency.
A large peak on the curve means that less current is drawn at the frequency of the peak. This can happen at frequencies where the loudspeaker system is resonant, i.e. vibrates naturally.
Other frequencies require much more current to produce the same sound pressure level. Low spots on the curve represent frequencies where maximum current is drawn from the amplifier, i.e. where the amplifier is under a greater load.
The low values should be used when determining the required gauge of loudspeaker wire that should be used, or how many loudspeakers can be run in parallel.
Impedance is also required to calculate how much amplifier power is delivered to the loudspeaker, which in turn allows the loudspeaker’s power handling limits to be assessed. This is a good example of where a single number impedance rating (often called the nominal impedance) serves as little more than a guideline.
The impedance plot paints a much better picture of impedance and the other ratings that come from it.
Always remember to use specification sheets for what they’re intended – determining the suitability of a product for an application.
They are not a substitution for listening and measurement when evaluating products and should not be the final word in the buying decision.
A famous physicist once said, “The data on a spec sheet may be the best data they ever took or the only data they ever took!”
Pat Brown teaches the Syn-Aud-Con seminars and workshops. Synergetic Audio Concepts (Syn-Aud-Con) has been a leader in audio education since 1973. With nearly 15,000 “graduates” worldwide, Syn-Aud-Con is dedicated to teaching the basics of audio and acoustics. For more information visit their website.