UNDERSTANDING FREQUENCY RESPONSE

If you're new to the world of audio and recording, it pays to know how frequency response affects what you do

by Craig Anderton

Sound is essentially a rhythmic variation in air pressure. This phenomenon resembles ocean waves, except that instead of having crests and troughs of water, we have crests and troughs of air pressure. But not all sounds are alike. Some are bassy, some are shrill; some are loud and some are soft.

We can classify these sounds by their level (commonly called volume), and frequency. Frequency measures the changes in air pressure. If these pressure changes occur many thousands of times in a single second, then we're dealing with a high frequency sound. If the air pressure changes occur at a slower rate—say, only 40 or 50 in a second—then we have a comparatively low frequency sound.

Because of the wave-like motion of sound, each "wave" (the crest and trough) is called a cycle. We measure frequency by counting how many cycles occur in a single second; this gives us a figure in cycles per second.

In 1960, the term "cycles per second" was replaced with the single word Hertz (abbreviated Hz), to commemorate Heinrich Rudolph Hertz (1857 - 1894), a scientist who contributed much to the subject we're discussing. For higher frequencies, the term kilohertz (abbreviated kHz) stands for 1000 Hz. Thus, a 1000 Hz tone has the same frequency as a 1 kHz tone.

Level defines the sound's loudness or softness; so if we know a sound's frequency and level , we have at least a vague idea of the type of sound we're talking about (in practice, though, sounds are complex and comprise numerous frequencies at numerous levels).

Now that we've defined our terms, let's move on to frequency response.

FREQUENCY RESPONSE

Frequency response is a characteristic associated with audio equipment. Since everyone has a set of ears, that's a pretty universal piece of audio equipment to examine first. Our ears respond to frequencies over about a 10 octave total range, from approximately 20 Hz to 20 kHz; but unfortunately, these figures only hold true for the ears of a relatively healthy youngster. As we get older, our ears lose their ability to respond to high frequency sounds.So, at a very advanced age we could have a response that tops out at 5 or 6 kHz.

Because most ears respond differently to different frequencies, ears are an example of an uneven frequency response. Now let's take this concept a step further. If the ear was a perfect listening machine, and if a sound source (loudspeaker or whatever) produced tones from 20 Hz to 20 kHz at exactly the same level, then our ears would respond equally to these tones; the high frequency ones would sound just as loud as the low frequency ones. This would be an example of flat response—i.e., the response would be even throughout the audible frequency range. But as we've already seen ears are imperfect, which means we have to deal with a deviation from flat response.

The ear also exhibits a different frequency response at different sound levels. At fairly low listening levels, the ear responds less to very high, and very low, frequencies. On the other hand, at high listening levels the ear's response is much flatter, although it's still not ideal. So much for the problems inherent in our hearing...it would be great if these were the only problems we had to deal with, but unfortunately, there are also other trouble spots in the audio signal chain.

A speaker never has a flat frequency response; no matter how much you spend, every speaker will deviate to some degree from an ideal response. For example, at very high frequencies a loudspeaker has to create very fast variations in air pressure—but the mass of the speaker's cone, friction problems, and other error sources make very accurate high frequency reproduction difficult. At the other end of the audio range, you have low notes that require the movement of large amounts of air. Even a 15" speaker can have trouble moving enough air to generate massive air pressure changes, thus reducing the low frequency response.

A typical loudspeaker's frequency response rolls off towards both the extreme high and low ends, but that's not all: resonances (response anomalies) in the speaker and speaker enclosure itself can cause deviations in the midrange response. To complicate matters even further, the room in which you are listening to the speaker will also change the response. A room with many hard surfaces (concrete, glass, etc.) will bounce high frequencies around and make them appear more prominent, while a thickly carpeted room will absorb many of the high frequencies. And we're not done yet...headphones, microphones, and other transducers that convert mechanical energy to electrical energy also introduce their own deviations.

Amplifiers don't have perfect frequency responses either, but compared to our ears (or loudspeakers), they're excellent. Many amplifiers can reproduce tones from 20 Hz to 20 kHz, or even 100 kHz, with ruler-flat response. Generally, the amp will not be the weak link in an audio system.

WHY FLAT RESPONSE IS GOOD

We're reaching the moral of the story: with so many variables between the sound source and the listener, we have to do something to keep the chaos to a minimum. Hence, whenever possible, we try for audio systems that have the flattest possible frequency response. Then, the only variables left are the listener's ears and acoustic environment.

Professional recording studios count on accurate monitor speakers and acoustically treated rooms to provide as flat a frequency response as possible. If a mix plays through a listening system with flat frequency response, then the listener will hear what the recording engineer heard while mixing. But if the studio loudspeaker exaggerates the high frequencies, then any recordings made at that studio will probably sound deficient in high frequency response when played over a system with a truly flat response. For this whole process to work smoothly, both the recording and playback systems need to have a flat frequency response.

But it's impossible for all systems to have a flat frequency response. As a result, when recording it's important to create a mix that sounds good on a variety of systems. Recording studios will often have small, imperfect "real-world" speakers right next to their standard, high quality studio monitors, thus making it easier to create a recording which sounds acceptable over both types of speaker. This may require a compromise—for example, the sound might be a shade too bright on the good speakers and not quite bright enough on the real-world speakers; but this is better than having just the right amount of brightness on the good speakers but an overly dull sound on the “real-world” speakers.

Now let's relate what we've learned to the real world. For example, if you want to check out a speaker's frequency response, you'll see a graph with squiggly lines all over it and strange markings given in "Hz" and "kHz" (which we already know about), and decibels (which we'll cover next; see Fig. 1). Interpreting this type of information is important when trying to compare audio equipment.

Fig. 1: This typical speaker response graph shows level on the X (vertical) axis, and frequency on the Y (horizontal) axis. Note the dropoff at the highest and lowest frequencies, and a bit of a midrange emphasis around 2 – 4 kHz.

THE DECIBEL

Let's examine another important technical term: the decibel (or dB). Actually, there are several different kinds of dB, and a complete treatment of the subject could take up a book. So, for now let's deal with the dB in general terms. Simply stated, the dB is a unit of ratio between two audio signals; probably the best way to become familiar with the dB is through some examples.

Suppose we're listening to an amplifier/speaker combination, and have a sound level meter calibrated in dB that registers changes in the system's acoustic output. Furthermore, suppose the input to the amplifier is not a complex musical source (such as a recording), but instead is a very pure audio test tone that can vary in frequency from 20 Hz to 25 kHz.

Remember, because the dB expresses a ratio, we're going to need some kind of standard signal to which we can compare other signals in order to derive this ratio. Under ideal circumstances, you would adjust the level of the tone for a comfortable listening level, and adjust the sound level meter so that it reads "0 dB" at this reference level. Notice that already there's a big advantage to working with the dB: the absolute sound level coming out of the speakers is not important, so we can listen at any volume level. What we're looking for are changes in volume level compared to the standard reference signal. The amount of change is a ratio, which is then expressed in dB. A signal that is stronger than the reference creates a ratio that is + so many dB, while a signal that is weaker than the reference creates a ratio that is - so many dB.

1 kHz is a common reference frequency because as mentioned earlier, the greatest response anomalies occur at the limits of the audio spectrum; 1 kHz lies in the nominal "middle" of the audio range. So, we have our reference frequency (1 kHz), and a reference level (0 dB). Now, let's vary the test tone frequency as we monitor the output of the amplifier/speaker combination with the sound level meter. Because no speaker is perfect, it's pretty safe to assume that the output will vary somewhat at different frequencies. Typically, in the lower regions (below around 125 Hz) the response starts dropping off and becomes relatively uneven.

A typical speaker's response might be summarized as varying no more than 6 dB from 60 Hz up to about 18 kHz. A spec sheet would thus indicate the response as "plus or minus 3 dB, 60 Hz - 18 kHz." This response would be typical of a medium size bookshelf speaker.

Knowing the speaker's response is important if we want to obtain the most accurate sound from our monitoring system. For example if we know where the speaker is not flat, we can flatten out the speaker's response to produce a more accurate monitoring system by adding an equalizer set to compensate for any frequency response aberrations.

However, specs tend to present products in the best possible light. Two speakers could have identical printed specs (such as plus or minus 3 dB, 50 Hz to 18 kHz), but one could have a much smoother response with just a dropoff at the extreme high and low frequencies, while the other looks like a relief map of the Alps and has all kinds of midrange peaks and dips that affect the sound.

The point of all this is that we often take devices such as loudspeakers for granted. However, suppose you're doing a dance mix and listening to it over headphones or speakers that “hype” the bass. The mix will sound somewhat bassier than it should due to the emphasized bass, so there might be a tendency to trim the bas back a bit. So far, so good—but if you then play the recording over a speaker with flat response, the sound will have less low end than what you were used to hearing because you had trimmed the treble back not to compensate for a defect in the microphone, but for a defect in the monitoring speaker. As a result, professional recording engineers often "learn" the speakers they are using. For example, if you know that your speakers are somewhat light in terms of bass response and you boost the bass to where it sounds right over your system, the sound will be bass-heavy on speakers which have a better low end response. So, you'll know to be conservative with the bass, knowing it will sound right on flatter systems, and not sound too boomy on systems that hype the bass somewhat.

All these potential variations explain why a major goal of mixing and mastering is to make recordings that “translate” over any system, from cheap earbuds to an audiophile's dream system. It's not an easy task, but if you make sure your own listening environment has a flat and predictable frequency response, you're off to a good start.

Craig Anderton is Editor Emeritus of Harmony Central. He has played on, mixed, or produced over 20 major label releases (as well as mastered over a hundred tracks for various musicians), and written over a thousand articles for magazines like Guitar Player, Keyboard, Sound on Sound (UK), and Sound + Recording (Germany). He has also lectured on technology and the arts in 38 states, 10 countries, and three languages.