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.