The focus of this article is in two areas. How to measure the frequency response of a subwoofer without sophisticated equipment and what you should measure when you want to replace your speakers. We’ll talk about different types of measurements that we can use in order to get the amplitude right and avoid sound interference within a given space.
The frequency range we’ll focus on will go from 30Hz through 300Hz. With replacement speakers, we’ll look at how to ensure that the speaker you are choosing will fit into the box that you already have. It’d be a heartbreak to invest so much money in getting a speaker only to discover that it doesn’t match your box.
Ways to Measure Frequency Response
There are six ways of measuring the frequency response of a low-end woofer which we discuss. If you use them properly, you’ll get the right results. They include Crane Measurement, Ground Plane measurement, Windowing, Anechoic Chambers, Near Field Measurement, and Half-Space Measurement.
Anechoic chambers or chambers that do not have echoes are those ones that the percentage of acoustic energy that they send back to the lumen when they hit the damping material in the box is less than or equal to 1%. What we want to achieve here is an acoustic space where we can get different acoustic behavior of loudspeakers in free field. Some of those behaviors include directionality, frequency response, and distortion – among others.
The environment of free field that is needed for this anechoic chamber hold in the case when the sub is seen as a one-point source that is spreading out in spherical patterns (i.e. 4π) into it. This is because when we have a wavelength (λ) that is spreading out sound larger than the greatest dimension of the sub itself, then it acts like a point source.
The mic used for this measurement is placed as far away from the subwoofer as allows it to stay within the section of the sound field of the sub with a dropping sound pressure level. With each distance that doubles, -6 decibels drop from the sound pressure level. Thus, we’ll say the mic is within the far-field of the subwoofer.
It’s difficult to completely imagine, or actually even, incorporate the true characters of an anechoic chamber into our real-life experience since it tends to be almost free from sound reflection (a contrast to the daily noise that we have to live with).
However, it is actually the condition of daily noise that is our experience that causes us to feel this difference in sound reflection which is artificial in itself. This artificial condition is the perfect one if we must get the correct data that we need in order to measure the different behaviors of the subwoofer’s acoustics right.
It is practically more difficult to design an enclosed space that is without an echo in a low frequency sound range than it is to design one in mid-range or high-range acoustics. If we can get the echo down to 1%, then our anechoic chamber has a practical low frequency limit that can be used.
The low frequency behavior of an anechoic chamber is determined by conditions such as: how the density of the damping wedges inside the enclosure is distribution through it, the total dimensions round the box plus its closed-up volume, the acoustic and mechanic make-up of the wedges, with the DUT size. For an enclosure to be used to reflect frequency range of 30Hz approximately, then the internal volume should be more than 4700m3 while the sport wedges should be no less than 3m deep, approx.
The principle that guides how an anechoic chamber is built is that the boundaries that make the chamber work only as acoustic loads for resistance and absorb plane waves in progressive motion. This principle assumes that the waves hit the absorptive face of the chamber, and they carry some real acoustic impedance (Z).
However, limits are placed for low frequencies because the condition for this principle to hold is a bit tricky for a subwoofer to attain. Basically, this is true if there is sufficient distance for the waves diverging in spheres from a source so that the boundaries can receive the plane waves in progression.
How much sound energy an anechoic chamber can absorb and give out reduces as it goes from 30Hz to 10Hz. However, you can increase the LF limit of any chamber by adding to the linear dimensions and also the density of its absorptive sections. If you are working on a budget, this measure might be high-handed for you.
Something else you can do is build a surface is absorptive in such a way that at low frequency their boundaries are reactive but at both high-frequency and mid-frequency, the boundaries act resistive. The absorptive sections here are set in a series of blocks with varying weights and sizes so that the boundary surface is reactive and resistive. This is called an acoustic jungle.
In practical terms, there are many obstacles to using the anechoic chamber when measuring the performance of your subwoofer. It may not even find one plus renting it may be very expensive. All the same, the perfect environment to use when measuring your sub indoor is the anechoic chamber.
This measurement environment is used outdoor and is as good as the anechoic chamber if it is used well. On the other hand, you have to be ready to contend with the noise pollution that follows and any weather conditions that present. If you have good weather and enough control of the noise in the background, the next thing to think of is the best condition to get the right measurements.
Use a crane to take your sub high off the ground. You can put it on a pole or stand as long as it is not close to the ground. You should observe some safety measures in mounting the sub away from the ground, even though it’s better to take very far from the ground. You just want your subwoofer to stay far away from any reflective boundary that can possibly muddle the response from it.
Truth is, it’s almost impossible for you to take the sub as high as it should go since there’s a lot of distance involved. For example, to access a wavelength of 20Hz, you have to go as far as 17m. Yet, if you are able to get the sub high up enough, you’ll have a perfect outdoor anechoic environment. You can get accurate and clean data from this measurement which you can use to design correction files for mics.
Since you may not have a tower to raise your subwoofer on (so that it’s not in contact with any surface that reflects sound), you can skip this method. We’ll discuss other less expensive ways to measure the performance of your sub.
Video: How to Measure a Subwoofer
This video discusses how to measure the performance of a subwoofer
Ground Plane Measurement
This measurement is done outdoors so your subwoofer and microphone will interact with environmental factors like noise. You’ll have to keep the sub on a flat, solid surface that is free of all obstacles so a driveway will be a good fit. Noise has a great potential to mess up a rather good measurement of amplitude response. The noise may be coming from the wind or from ground traffic. You can tackle the situation by taking an average of measurements made in different situations. A better remedy would be to take the measurement when the environment is totally quiet.
When taking the Crane Measurement, the aim is to get rid of all kinds of interference and reflection from any surface, so you mount the sub on a height that is totally off the ground. With the Ground Plane method, you have to consider the one parameter where the subwoofer stands. The sound signals that bounce back from the ground is the other source (though virtual) that is akin to the original sound. This method has scientific roots and that is seen in the formula used to calculate how big the RMS of sound pressure is.
The parameters here represent the following:
|p| = size of sound pressure’s RMS
A = size of sound pressure’s RMS one unit away from the midpoint of each sound origin
r = distance of measurement
b = distance from the midpoint of the original sound image to the midpoint of the virtual sound image
λ = wavelength of the frequency you are working on
θ = perpendicular angle that cuts through the sound images – virtual and real
So, with this formula, we measure sound pressure from 2 sources: the virtual sound image and the real sound image.
When we have long wavelengths such that λ is >> b then b is small relatively while the two sound sources will be seen as one source such that the sound pressure is now twice the pressure of the main source. (At long wavelengths, we have low frequencies.) When the sound pressure is doubled, we get a rise in the sound pressure level measured within an axis (as much as 6dB) compared to what we get from the same subwoofer when we use the anechoic method that is free from interference.
An important precaution to take is to make sure that you don’t have any big object or surface that is within a radius of –
– when you take the measurements, except the ground where the subwoofer stands. Large objects may represent anything from a building to a tower.
It’s easy to set up your materials in the ground plane method. First, place your sub on the ground in such a way that the speaker faces the microphone you are using for your measurement. This would mean laying the sub on the side.
Follow by inclining the box in a position that allows the middle point (where the speakers are fastened) to face the ground at a distance of 2 meters. If you have a laser pointer, that will help. When you’ve got the placement, keep the mic you’re using to measure at the post where the ground and middle point meet. Then take your measurement.
It’s possible to measure the response from 1m distance but a combined reflection from the virtual and acoustic image outputs at the mic creates a sound pressure level (SPL) of 6dB. If the distance is increased to 2m, the SPL from that point reduces by 6dB. This allows the result gotten from each point of interest to imitate the result if you were measuring with an anechoic chamber with a few variations.
This is a cheap alternative to using the anechoic chamber if you don’t have one and it saves you the stress of mounting the sub on a 100-inches tower for measurement. You can regard this as the best measurement option because it’s easy to apply.
The practice in this method is to position a loudspeaker system’s front board or a driver that is not fixed yet inside, then use a big baffle to flush it. The idea is that by the time you change the main space from being spherical (i.e. 4π steradian) to being hemispherical (i.e. 2π steradian) the measurement you get from the amplitude response will show the system’s behavior at low frequency better within a listening environment.
Practically, when applying this method, you should use a big baffle that is not complex to test the driver, insert the system in a ground (or flat) space so that the driver faces up, then use the test surface to flush. You might decide to dig a hole and bury the subwoofer in a bid to measure the amplitude response, but this is not an effective approach. It’s not even every kind of system that can be buried in ground space. For example, the vented box and all the cables that run through it.
There are a number of reasons why windowing is a tool to choose when measuring the performance of your sub. The process employed is to use an MLS (Maximum Length Sequence signal) to measure the response of the sub before passing the response through some post-process utility. This produces frequency response plots, ETC curves, waterfall (otherwise called cumulative spectral delay plots).
The best feature that this method presents is that you can window out every part of the measured sound signal except an anechoic part. Practically, the limit to the use of windowing is that the low frequency result might not be so correct considering the condition of sound with the environment.
If, for example, you are measuring the behavior of your subwoofer in a room but have to window out data that is more than 10ms because of reflections. This means that you can only accept a full sinusoid period within that window that is no longer than 10ms. Data with longer wavelength periods will not be presented correctly and this will eventually affect the process later.
You can always find ways to accurately window out your measurements even in poor conditions. These include using a microphone that is especially for an environment in your measurement or using the concept of near-field when taking your time-windowed measures.
Near Field Measurement
If you do this well, you’ll have another efficient method to measure the response of your sub’s acoustic amplitude. This method comes handy if you can only measure your subwoofer indoors.
The formula is as follows:
pn = the highest pressure in the middle of driver diaphragm in near field
r = the distance between the mic position and the middle of the driver diaphragm
a = radius of the driver diaphragm
pf = the highest pressure within an axis taken at r (a distance far field of the driver diaphragm) and represented as
ρo = air’s density which at 20oC is 1.21 kg/m3
Uo = highest output of volume velocity from the driver diaphragm
k = wave number which is ω/c or 2π/λ
c = sound’s velocity in air which is 343 m/s
As a matter of fact, within a frequency of interest which is usually ka < 1, the sound pressure in the near field is proportional to the sound pressure in the far field. Again, near field measures do not rely on the sub’s firing space which allows you to measure near then scale it to far. Near field is at the correct upper-frequency boundary if…
Another good use of the Near Field Measurement is used in measuring the distortion of the system and the total sound power correctly. It’s efficient in measuring both passive and active subs, vented and closed systems. This measurement method is such that you have to keep the measuring mic at a point where it is centered on the dustcap of the driver and perpendicular to it. The mic should also be within a distance of .11a from the midpoint of the driver if your aim is to get a sound pressure that is ≤ 1 dB.
For vented systems, the acoustic output of the port and driver (even if they are multiple) should be measured differently from each other. In measuring the ports, your mic should be placed in the center of the duct port and normal to it. Use the faceplate of the system to flush it.
If the system is an enclosed one with just one driver, then you have to scale the data you get from the near-field output measurement of the driver. Systems with more than one radiator require you to measure each of the radiators then put the results of the individual measurements together to get the amplitude response of the entire system. [Radiators can be drivers, passive radiators, or ports]. Scale the data from your measurement to a reasonable distance which would be between 1 and 2m.
Here’s how you can scale the data from your nearfield measurement to 1m:
Take Sd as the radiator’s effective diameter which is m^2
[You can calculate anechoic far-field equivalent of 1m with the formula above and remove 6dB from whatever you get.]
Alternatively, you can use the formulas below to scale NF data to FF.
FFdB = dB value scaled from far-field (FF)
NFdB = dB value scaled from near-field (NF)
d = the distance where you should calculate the values for far-field from (an example is 1m)
r = the radius of the radiator that is most effective
In all of these measurements, whatever unit you use must be consistent for the radius and the distance. The farther apart drivers are from ports (with regards to wavelengths), the more complicated the calculation is.
You just have to be sure that your measuring mic has the ability to stand the radiators’ acoustic output within a close range, especially if you’re testing an SPL output at maximum dB. Run a few tests to be sure of your driver’s excursion before you get on with the main measuring.
Talk to You Later
Hopefully, in the next few articles, we’ll talk about how to measure your speaker if you want to change the driver of your subwoofer system. One tip is that you can install a new driver in the old enclosure. Save some money from your subwoofer upgrade plan.
I hope you found the information here useful.