Identifying Legitimately High Fidelity Loudspeakers: Power Response & Baffle Step

Regarding half-space measurements, they originally were the result of Acoustic Research’s (AR’s) exhaustive measurements back in the 1960’s. AR was one of the first speaker companies to do detailed, repeatable scientific speaker measurements and publish them with accurate explanations that the average consumer could understand. Back then, many speakers were in fact mounted on “bookshelves,” with books all around the speaker, constituting a measurement environment that did, indeed, approximate a true 2 Pi (half-space) environment.

When that same speaker was mounted on a stand somewhat away from the major room surfaces (the side wall, the wall behind it, and up from the floor below it), the speaker would exhibit what today we call the “baffle step” phenomenon.

The above curves of the famous AR-3a from 1968 clearly show that. In the top figure, the 3a is in a pure 2 Pi environment (“bookshelf,” surrounded by books), and its LF-to-midrange response is smooth and predictable.

In the lower curve, the 3a is stand-mounted away from the walls. You can clearly see the lowering of the woofer’s response level as the frequency transitions from a 2 Pi environment (in the midrange, where the speaker’s baffle is large enough to provide that environment) to a 4 Pi environment in the lower bass. Interesting that AR recognized this and identified it in 1968. They were ahead of their time. But not until Roy Allison’s Allison speakers of 1974 were there speakers that took this into specific account. Allison’s 1973 AES article The Effect of Room Boundaries on Low Frequency Power Radiation is particularly illuminating.

The concept of Power Response vs. On-axis first arrival frequency response is regarded by many as way to take this entire matter into consideration with measurements. By measuring the speaker’s total radiated output in all directions at all frequencies in the reverberant field (not just in the near field, 1M on axis), proponents of the Power Response approach feel that that is a more relevant, realistic way to characterize and predict how a speaker will sound to a listener in a real room, under real-world conditions.

Boiled down into simple terms, the first-arrival crowd feels that the on-axis, first-arrival “anechoic” frequency response is what the ear grabs onto first and that sound is the primary determinant of a speaker’s essential sound/tonal quality. They feel that the room reflections, driver interaction, phase considerations, etc—however closely in milliseconds those reflections and artifacts may follow the ‘first arrival’—are separated out by the brain/ear system and what you fixate on is that first arrival.

Balderdash, says the far-field power response crowd. The room reflections etc. are so close in time to the first arrival that they swamp the first arrival completely, leaving the overall far-field energy output of the speaker—the so-called “power response”—as what you hear to determine the tonal quality of that speaker. Only if you sit very close to the speaker—say, within 2 or 3 feet, on axis—does the first arrival response really count. Once you’re back about 6-8 feet (ie. farfield of the speaker), most of the first arrival sound is simply folded into the far-field power response.  It is the far-field response and more specifically the early reflections from the sidewalls that dominate what we hear in small room acoustics.

Of course, the two are not mutually-exclusive. As a speaker designer, you can reduce near-field diffraction, correctly align your drivers, etc, do all kinds of things to optimize the near-field first-arrival sound without hurting or negatively affecting the far-field power output. That is what most good speaker designers do—they optimize the near-field response “just in case” it makes a difference.

Test it Yourself

There’s a great test you can perform yourself at home that perfectly demonstrates the difference between near-field and far-field response. You don’t need any expensive test equipment. As a matter of fact, you don’t even need a Radio Shack SPL meter.

You need a pillow. Preferably, a sofa pillow, maybe 12” x 12” or so. That’s it.

Here’s what you do: sit close to the speaker, about 2 feet away. Play only one speaker. Use some full-range music that is rich in upper-midrange and treble content. (Jazz is good for this, because it has lots of cymbals, “reedy”-sounding saxophones, and piano upper harmonics.) 

Listen to the music. Now hold the pillow up in front of your face so that your line of sight to the speaker is blocked.

Lower the pillow away from your face. Note the difference in the sound depending on whether the pillow is raised or lowered. When the pillow is raised in front of your face, the speaker’s sound becomes noticeably duller and muffled. This is because the majority of the high frequencies reaching your ear are the result of the speaker’s direct radiation, right from the tweeter to your ear, on a straight line. So when the pillow is raised, it blocks and absorbs those highs, and you can’t hear them. This is the “near field,” and what the pillow is interfering with is the so-called “first-arrival” sound.

Now move back to your normal listening position, about 8-10 feet away from the speakers. Repeat the test: Play the music and listen with the pillow sitting on your lap. Now play the same music and raise the pillow in front of your face. You’ll notice something pretty surprising: the sound is almost (note: not absolutely) identical whether the pillow is raised or lowered. This is because you’re now sitting in the far field, and almost all the high frequencies are reaching your ears by way of room reflections and indirect sound—not on a straight line like in the near-field example.

The wider a speaker’s high-frequency dispersion, the more this will be true, because a wide-dispersion speaker generates more room reflections than a narrow-dispersion speaker. As a generalization, one could say that a speaker with a 1” dome tweeter will generate more room reflections than a horn speaker with an intentionally limited radiation pattern.

So all those near-field considerations like driver alignment, cabinet diffraction, phase relationships, etc. are far less important in real world listening conditions than their theoretical importance might suggest.