# Why Do Frequency Response Curves Matter?

By Ray A. Rayburn

No one can look at a frequency response curve and tell you "this is a great sounding loudspeaker (or microphone)" just based on the curve. The issues involved in going from a frequency response curve to the subjective "sound" of a particular loudspeaker or microphone are far too complex to reduce to any fairly simple measurement like a frequency response curve.

On the other hand, once you learn to understand frequency response curves, they will tell you a lot about the sound of a loudspeaker or microphone. In some cases you will be able to look at a curve and say "this is a bad sounding loudspeaker" based on the response curve, even though you can't do the opposite.

The first thing to understand is what the horizontal and vertical axes mean. The vertical axis is usually the sound level in dB. Louder sounds are higher up, while quieter sounds are lower at any given frequency. What is important in a frequency response curve is not what the actual numbers are, but how much they vary from frequency to frequency.

To understand this we need to understand a bit about the dB or "decibel". The dB uses a logarithmic scale since this correlates fairly well with human hearing. As a rough rule of thumb, a change of 3 dB at mid frequencies is just noticeable by the average person. Now some people have trained themselves to hear much more subtle differences. I once worked with a record producer who could hear differences as small as 0.1 dB at some frequencies. I would say that a well trained audio engineer or audiophile can detect subtle differences in frequency response as small as 0.5 dB at some frequencies. However, the average person will probably not notice changes until they are around the 3 dB different point. This ability to detect differences gets worse for everyone at low and high frequencies.

A larger change on the order of 10 dB is needed for something to sound "twice as loud" at mid frequencies. This subjective impression seems to hold up fairly well for all listeners. Therefore, an increase of 20 dB will sound four times as loud, and an increase of 30 dB will sound eight times as loud.

Some folk get confused since an increase of 3 dB is twice the power, and an increase of 10 dB is ten times the power. This is true, but does not change the way the ear / brain combination interprets sound. For example people want their sound system to play louder and buy a 200 watt amplifier to replace their existing 100 watt amplifier, and think it will sound twice as loud since the power has doubled. The ear, however, says "that's just a bit louder" since the level increase is just 3 dB. In order to get the sound system to sound twice as loud, they would have to buy a 1000 watt amplifier to replace the original 100 watt model (a 10 dB increase in level). Then they will probably find they are burning out their loudspeakers trying to get the system to play twice as loud.

The next thing to understand about frequency response curves is that they can have many different scales on the vertical axis. I mostly publish response curves with a 30 dB difference from top to bottom, but many different scales can be used.

For example, if you look at this next response curve you might think it varies a lot.

While if you look at this next curve you might think it is very smooth.

Actually both curves are of the same measurement, just presented at different vertical scales. The first curve was done at a scale of 10 dB over the entire vertical range, while the second curve was done using an 80 dB vertical scale. To allow easy comparisons, I present all my curves using a 30 dB vertical scale unless otherwise noted. Here is the same curve using a 30 dB vertical scale.

So now we understand that the important thing on the vertical axis is not how much the curve appears to go up and down, but the number of dB it goes up or down. Be careful when comparing curves to look at the dB scale. If no dB scale is given, then the curve is meaningless.

The next thing to look at is the horizontal axis that shows the frequency. The usual numbers given for the range of human hearing is from 20 Hz to 20,000 Hz (20 kHz). This range can be expected to hold true for healthy young people who have not been exposed to excessively loud sounds. Most of us lose some of our hearing starting at the frequency extremes as we age. Loud sounds, disease, and even some drugs can accelerate this natural process of hearing loss.

Low frequencies as given in Hz (Hertz) are the low pitch sounds we hear. For example the low note on a bass guitar is around 40 Hz. Cymbals contain many high frequency sounds mixed together, extending well past the nominal limit of human hearing of 20 kHz. A very deep bass singer might go down as low as about 80 Hz. The most critical frequency range for the intelligibility of human speech and singing is from 2 kHz to 4 kHz. Sibilants in the human voice go up to about 12 kHz.

Most of the frequency response curves I present start at no lower than around 200 Hz. This is due to the difficulty of measuring the low frequency performance of a microphone or loudspeaker without having the room changing the measurement. Accurate measurements at low frequencies of just the response of a microphone or loudspeaker without the room intruding on the measurement requires either a very large room or an outdoor measurement setup.

If we were looking for the "perfect" frequency response that showed us the loudspeaker or microphone made no change in the sound level at different frequencies, that response curve would be called "flat". Here is an example of a flat frequency response curve.

Note that at the 0 dB level there is a perfect horizontal line.

Now even if there were a real device that had this response curve, that would not by itself make a perfect device. First, audio engineers use loudspeakers and microphones much as a painter might use different paints and brushes. Every device has its own "color" and "texture" which the skilled engineer uses to produce a pleasing result. Second, most frequency response curves are only of the response directly in front (on-axis or zero degrees) of the device being tested. Even if the on-axis frequency response were flat, that would not tell us what the response was like at different angles. Most loudspeakers and microphones will have very different responses at different angles. The minimum set of curves needed to characterize a microphone's variation in frequency response and level at different angles is on-axis, 90 degrees (directly to one side), and 180 degrees (directly to the rear). Loudspeakers are generally more complex, and require more measurements to fully characterize.

Here is an example of a set of response curves for a microphone.

The white curve on top is the on-axis frequency response. The yellow curve shows the reduced response at 90 degrees to one side, while the purple curve shows the response to the rear of the microphone. As you might have guessed, this microphone has a "cardioid" or heart shaped directional pattern. Over much of the frequency range the response at 90 degrees is similar to that on-axis, just at a somewhat reduced level. The microphone provides considerable rejection of sounds arriving from the rear at low and mid frequencies. Where things get interesting is at the higher frequencies where the pattern that held at lower frequencies no longer holds.

Overall, this shows how the sound color of the microphone varies with the direction a particular sound approaches the microphone. It also shows that there is a fairly broad range of angles in the front of the microphone where the sound pickup does not change very much. Even at 90 degrees, the level is down only 5 dB over much of the frequency range. At the highest frequencies the pickup angle with respect to the front of the microphone has narrowed, and as a result the frequency response at 90 degrees rolls off at the highest frequencies.

Like many microphones, this mic has a frequency at which there is only a small difference between the on axis, 90 degree and 180 degree levels. Some microphones have more than one frequency at which this happens. When a mic is used in a sound reinforcement system, frequencies at which there is less rejection of sound from the rear and sides will be more likely to feedback. Almost all directional microphones have such frequencies, so it pays to be aware of them.

Please be aware that the response of a loudspeaker or microphone can change with time. Microphones are subject to damage from dust, dirt, heat, and spit among other factors. Over-driving often damages loudspeakers.

If you had two loudspeakers or microphones with identical shapes to their response curves, but as measured under identical conditions one had a rougher or more jagged response curve, then it is likely that the device with the smoother curve would sound subjectively better to the ear. In practice making such comparisons is very difficult and nearly impossible using many manufacturer's published curves.

First it is unlikely that any two manufacturers are using exactly the same technique and test setup for measuring their products. Second, published curves are almost always averaged to make them look smoother. For example here is a raw measurement I made followed by the averaged measurement as it might be commonly published.

You will notice that the smoothed curve has lost all the details that show you a lot about the sonic character of this microphone. This example used an extreme 2 octave wide averaging, but averaging ranging from 1/3 to 1 octave is common. I only publish raw curves as I measured them unless specifically stated differently. Even my measurements have an inherent amount of averaging due to the measurement technique used. Right above the curve on all of my measurements is a number specified for Frequency Res (Resolution). Do not try to compare the fine detail of two measurements unless they were taken with the same frequency resolution.

Lastly you will find frequency response curves published that were created either out of someone's imagination, or by some artist manually tracing the measured curve to make something nicer looking for publication.

It can be very educational to compare the subjective "sound" of a microphone or loudspeaker to the measured response, particularly if the response is detailed and not averaged. Over time you will learn to correlate the bumps and dips in a response curve with the sound you are hearing. This in turn can help you understand your microphones and loudspeakers better, and help you determine how to get the most out of them.

Now there are other things that effect the sound besides the frequency response. Microphones like everything else add distortion to the sound. In particular they add harmonics and intermodulation distortions. These distortions can exist at all levels, but tend to get worst at high levels. All mics tend to have distortion that increases with level as the mechanical moving parts get stretched farther from their resting positions. Then as the mechanical motion limits are approached the distortions go up suddenly. Condenser mics add electronics which can add their own distortions to the mechanical limitations of the pickup cartridge itself.

Most microphone frequency response measurements are made at a distance of around 3 or 4 feet. From such a distance and out to greater distances the frequency response of a microphone is close to constant. When we are measuring a directional microphone, the response changes as we get closer to the mic. This is the well known "proximity effect" that causes a bass boost in the frequency response of the microphone at close working distances. This boost changes very rapidly in the last few inches before the sound source touches the mic. For these reasons it is very hard to accurately measure this. It does, however, make an important part of the "sound" of the microphone as many mics are used close to the sound source and not exclusively at a distance.

One issue that I touched on above is that the response is not the same at all angles. Since most of us do not use a microphone on-axis only in an anechoic (echo free) chamber, but instead in real rooms with reverb times and reflections coming into the microphone from all angles, any look at 1 or even 3 response curves of a microphone is only telling us part of the total picture.

You could ask why it is not best to use a flat response microphone, and get the sound you want through EQ?

The only mics that approach flat are certain Omni models. Since we often need directional microphones (although maybe not as often as many folk think) we are always dealing with microphones with sonic colorations. The approach of using a flat mic and EQ to get the sound we want assumes that the response differences at different pickup angles are not important, but they are an important part of the characteristics of a microphone.

For classical recording where I am trying to accurately capture an acoustic event, I will try to use as flat a mic as I can. For most other uses of microphones a microphone's color can be an important tool in getting an interesting sonic result.

Some companies are selling "microphone modeling" devices that are claimed to be able to turn the sound of one microphone into that of another. These units use DSP based filters to modify the on-axis response of one microphone to match that of another microphone. These will only somewhat approximate the differences in sound of the two microphones. Among the limitations of this approach are:

How detailed a frequency response was used to produce the difference filter? If it was not very detailed, it will lose much of the subtle sonic differences. If it is detailed, it is likely that it does not very well match the response of your sample of the microphone in question, and thus imposes the difference in response of your mic from the mic they measured onto the output sound of the new mic it is trying to approximate.

(Microphones differ in response from sample to sample when new. Used and abused microphones can have much greater differences. Matched pairs of microphones must always be treated with care so they don't change in character and lose the match.)

"Microphone modeling" has no way of dealing with proximity effect. This effect can be very different for different models of microphones and for different distances. In particular it has very different characteristics between common dynamic mics and large diaphragm condenser mics. This is part of the sonic differences that account for some of the mystique around large diaphragm condenser mics and their sound.

"Microphone modeling" can at best only compensate for differences in the on-axis response of a microphone. However, real microphones have different responses in different directions. While the microphone may be pointed at the main sound source, it also picks up the sounds of other sound sources in the room along with acoustic reflections and reverberation from all sources. Very little of this additional sound pickup is along the main axis of the microphone, and therefore has very different character imparted to it. A "microphone modeling" device has no way of knowing from what direction each part of the total acoustical input came from that resulted in the microphone's electrical output. Therefore it can't compensate for the typically very different frequency response of a microphone to sounds arriving from different directions.

Overall the claims made for such "microphone modeling" devices are usually vastly overblown.

To answer the original question "Why do frequency response curves matter?", besides all the information they can provide you, they tell you the manufacturer or reseller cared enough about the product they are selling to actually test every one to make sure they were performing optimally.

I have posted here scans from a GenRad manual. This includes lots of valuable information on the directional characteristics of "omnidirectional" microphones, difraction effects and other related microphone characteristics.

Ray is a member of the AES Standards working group on Microphone Measurement and Characteristics.

If you have comments or suggestions, email me at Ray@SoundFirst.com

Edited 10/15/2012

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