Size Matters: Observations On Loudspeaker Directivity

Physics hasn’t changed.... When it comes to pattern control, size still matters!
April 20, 2010, by Bruce Main


Trap boxes and line arrays get all the attention. And that’s no surprise - they’re big and loud, and dare I say it, glamorous.

But the truck rarely rolls without a complement of two-way loudspeakers sporting a 12-inch or 15-inch woofer and a horn.

Whether its monitor wedges, drum fill, front fill or just “speakers on sticks,” small 2-way boxes do many of the everyday jobs that make up a typical sound reinforcement day.

We take the performance of these boxes for granted, but they can be used to better effect if we really understand their directivity characteristics and what makes them perform the way they do. They’re often described as a 90 by 60 box or some other dubious reference.

But 90 degrees by 60 degrees at what frequency? Certainly not from DC to light.

There are four principle ingredients that govern the dispersion pattern of these loudspeakers, including the cone driver, horn, crossover and cabinet.

Let’s look at these one at a time and assess their contributions. Before we go through our list, though, let’s review some basics.

The amount of directivity any device can exert on a sound wave is directly related to the proportional sizes of the device and the sound wave.

To understand this relationship it is important to have a good grasp of how big or small a sine wave is at a given frequency.

Sound at sea level at 72 degrees Fahrenheit travels at approximately 1,130 feet per second. We express frequency or cycles (sine waves) per second as Hertz.

So if the frequency of a wave is 1 Hz, the wave is 1,130 feet long. Logically, a 10 Hz wave is 113 feet long, a 100 Hz wave is 11.3 feet long, and a 1,000 Hz wave is 1.13 feet long, etc.

While it’s not overly difficult to do the math to determine the wavelength of any given frequency, there is an old “cheat” called the rule of 5-2-1:

20 Hz = 50 feet
50 Hz = 20 feet
100 Hz = 10 feet
200 Hz = 5 feet
500 Hz = 2 feet
1,000 Hz = 1 foot
2,000 Hz = .5 foot
5,000 Hz = .2 foot
10,000 Hz = .1 foot

While not perfectly accurate, it fills the bill for “quick and dirty” calculations. Physics dictates that a source be physically large in comparison to a wavelength to exert directional control over it.

So let’s look at the low frequency directivity of a 12-inch driver in a 2-way loudspeaker with a 90-degree by 60-degree horn.

Matter Of Control
Remember that the low frequency driver’s only means of controlling the dispersion of the sound wave in a front-loaded loudspeaker are its cone diameter, and to a lesser extent, some boundary effects (we’ll discuss that later).

At 100 Hz, the driver is physically small in comparison to the 10-foot wavelength and provides almost no directivity (Figure 1).

If we increase the frequency gradually, the 12-inch driver does not suddenly exert pattern control over the sound wave when it reaches 1,000 Hz (1 foot), and is the same size as the driver itself.

Rather, it has more and more effect as the frequency gets higher and the wavelengths get shorter. (Figures 2 & 3)

Fig 1: Horizontal directivity balloon of a 12-inch 2-way loudspeaker at 100 Hz (box facing left)

In this frequency range (800 Hz as shown in Figure 3), the cone driver is actually providing approximately 90-degree horizontal dispersion.

But also realize that since this pattern is conical (the driver is round), it is not producing the specified 60-degree vertical pattern.

As the frequency increases the driver exerts more and more control until it begins to “beam” at higher frequencies.

But by the time it narrows that much, it’s above the crossover frequency.

This particular loudspeaker crosses over about a half-octave above the balloon in Figure 3.

Fig 2: Horizontal directivity balloon of a 12-inch 2-way loudspeaker at 500 Hz (box facing left)

This has an overriding effect on the polar behavior of the box, especially in the vertical domain, so we will discuss the range from 1,000 Hz to 1,500 Hz when we discuss the crossover. Now, on to the horn.

Dominate The Wavelength
There are multiple elements in a horn’s design that contribute to its ability to achieve pattern control at a given frequency.

Some of them are throat geometry, length and flare rate.

But the most obvious factor is the size of the horn mouth. The same rules apply here as to the cone driver. Size matters.

The horn mouth must be large enough to dominate the wavelength in question in order to provide complete directivity at that frequency.

So if a horn mouth is 6 inches wide by 3 inches tall it will be somewhat omnidirectional at 1,000 Hz.

Fig 3: Horizontal directivity balloon of a 12-inch, 2-way loudspeaker at 800 Hz (box facing left)

It will not dominate the sound wave until the frequency reaches about 2,000 Hz in the horizontal plane and 3,000 Hz in the vertical plane.

It may provide a 90-degree by 60-degree pattern above 3,000 Hz, but almost certainly not at lower frequencies.

Cone drivers and horns by themselves are fairly predictable devices. But combining the two in close physical proximity can be quite challenging.

The first problem is physical offset. In a typical 2-way box, the devices are located one above the other ,and may also be at different depths.

Even if we use delay to correct the time alignment between the drivers on axis, any other vertical angle will skew the time arrivals from the horn and the cone driver.

Because the bandpasses and vertical dispersion patterns of the drivers necessarily overlap in the crossover region it is probable that at any vertical angle that is off axis we will be hearing contributions from both drivers out of phase.

This means there will be lobes and nulls. (Figures 4 & 5)

This particular box was crossed over at 1,350,Hz with a symmetrical Linkwitz-Riley 24 dB slope.

These lobes will vary in direction and intensity based on driver offset and pattern control, crossover slope, and overlap and alignment delay settings, but they will always occur in multiple driver boxes with physically separated sources.

If a cabinet is laid on its side we get the same phenomena in the horizontal plane. Floor wedges, anyone?

This is one reason there has been a resurgence in coaxial boxes.

Fig 4: Vertical directivity balloon of a 12-inch, 2-way loudspeaker at 1,250,Hz, crossover at 1,350 Hz (box facing left)

Because there is no vertical offset between the sources, we only have to correct for the variation in depth between the acoustic origin of the cone and the horn driver, and that distance stays more constant with off-axis listening positions.

The trade-off is that many coaxial designs use the driver cone as the horn flare to guide the high frequencies, and while this may be fine for monitors or other near-field applications, more precise pattern control is often required for sound reinforcement duties.

Baffles, Boundaries
The final piece of the directivity puzzle is the cabinet itself and the boundary effect created by setting it on something. Fractional space loading is created when we decrease the space that a device is radiating into.

As we saw in Figure 1, low frequencies are omnidirectional, so when we set a loudspeaker on the floor, we effectively halve its radiating space at low frequencies. This produces an additional 3 dB of output (double the power) in the hemisphere that it is still exciting.

Fig 5: Vertical directivity balloon of a 12-inch, 2-way loudspeaker at 1,600 Hz, crossover at 1,350 Hz (box facing left)

If the baffle on the cabinet is physically large enough versus a given frequency, it can act as a boundary to create half space loading. This is what is sometimes called “baffle step.”

In modern cabinets, the baffle is rarely much larger than the driver that is mounted in it, because generally, priority is given to things like weight, truck pack, handle location, flying hardware, arrayability and profile.

Technology has gone a long way towards providing a ton of output and fidelity from small packages. But physics hasn’t changed. When it comes to pattern control, size still matters!

Bruce Main has been a systems engineer and front of house mixer for more than 30 years, and has also built, owned and operated recording studios and designed and installed sound systems.

Originally published on ProSoundWeb. Reprinted by permission.


David McLain | The Loudspeaker Guy | CCI SOLUTIONS
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Creating Professional Sermon Podcasts

Here is a very good, two-part "How To" video that shows how to use Audacity to edit your audio sermon recordings to make them sound professional. They'll also show you how to use iTunes to convert and archive your sermons as MP3s.

Download Audacity 1.2.6 for free from

By Derrick Jeror of HouseTop Media, and used with his kind permission.

This is a video lesson. As usual, if you have difficulty with the video on your mobile device, click on the title ("Creating Professional Sermon Podcasts ") or go to the CSG home page.
David McLain | The Podcasting Guy | CCI SOLUTIONS
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Understanding Sound System, Loudspeaker & Room Interactions

If one could listen to only the direct sound of a loudspeaker, the world would be a very different place!
by Sam Berkow

signal room interactions

If one could listen to only the direct sound of a loudspeaker, the world would be a very different place!

Unfortunately, free field listening, where you have NO reflections, room modes or ambient noise, is hard to achieve in everyday life, so we listen to loudspeakers in real rooms.

The interaction of a loudspeaker system and a room can be very complex to understand, model or measure! One way to measure this interaction is to measure the impulse response of the loudspeaker/room system.

The impulse response of a typical sound system in a room contains lots of interesting information, including:
1) The delay between the loudspeaker and measurement microphone
2) The direct sound-to-reverberent level ratio
3) The time arrival, frequency content and level of reflections of sound
4) The early and late decay rates of the sound
5) The frequency response of the direct sound.

This last point is particularly interesting. The question is “What do we want to measure and why?”

One question that goes to the heart of “system” measurement and optimization issues is “If the impulse response contains the frequency response of the direct sound, can we separate the loudspeaker response from the room response?”

Also “If we can, do we want to?”

Figure 1 shows an impulse response displayed in the time domain. The “spike” that represents the direct sound actually contains the frequency and phase information about the loudspeaker.

To see this information we must transform this portion of the impulse response into the frequency domain. To achieve this isolation of the direct sound from the room response, we must select a time window that includes the direct sound but excludes the reflections and decay of the room.

Figure 1: The impulse response of a 1250 seat multi-purpose hall. The x-axis is time (~0.75 sec) and the y-axis is magnitude in dB. Note the direct sound, reflections, the reverberant decay and the noise floor.

Figure 2 displays such a time window. This measurement was made using a full range loudspeaker system with the microphone approximately 60’ from the loudspeaker. Pink noise was used as a reference signal and the impulse response was calculated using a 512K FFT (although only the first ~0.75 seconds are shown).

Figure 2: The impulse response of a 1250 seat multi-purpose hall. The vertical lines suggest a time window that ignores most of the effects of the room at frequencies whose periods are longer than the time window (i.e. low frequencies).

We can take the “time windowed” data and transform it into the frequency domain using FFT mathematics. This transformation yields a result that shows how much energy is present at each frequency, as shown in Figure 3.

You can see the pronounced roll-off of low frequency energy. You can also notice the lack of LF resolution in this figure.

The lack of resolution at LF is offset by a excess of HF resolution.

This uneven resolution between LF and HF energy is the result of the FFT mathematics used to transform the data from the time domain to the frequency domain.

Standard FFTs yield data that is distributed linearly in frequency (one data point every X Hertz).

Unfortunately, humans perceive frequency logarithmically.

Figure 3: The frequency response of the direct sound portion of an impulse response of a 1250 seat multi-purpose hall. The response was calculated using a 512 point FFT (which equals a 512/48000 or ~11 msec). As you can see the frequency response shows a pronounced LF roll-off.

This lack of LF resolution in Figure 3 is a direct result of the use of a short time window in our transformation from the time domain to the frequency domain.

It is interesting to note that this plot does NOT correlate with what we hear. Simply listening to the full range loudspeaker system we were measuring made it clear that the system was reproducing LF energy down to at least 100 Hz!

I would suggest that a primary goal of an effective measurement system should be to provide results that correlate well with what we hear. So the lack of correlation between what we have heard and what we measured suggests a modification to our approach.

As an alternate approach to trying to find a measurement that correlates with what we hear, we can try using a longer time window to “see” the LF response with better resolution. A longer time window of approximately 250 msec is shown in Figure 4.

Figure 4: The impulse response of a 1250 seat multipurpose hall. The vertical lines suggest a time window that INCLUDES most of the effects of the room. The time window shown is approximately 0.25 seconds.

To transform this longer “slice” of the impulse response into the frequency domain, we will use an 8k FFT which represents 8k/48000 seconds, or 0.171 seconds. Notice again that this time window includes both the direct sound and the response of the room.

In Figure 5 the low frequency information is seen in adequate resolution, however the high frequency results look confusing. The plot shows data that has 5 Hz resolution (i.e. one data point every 5 Hz). While this resolution provides excellent LF resolution (between 31 Hz and 62.5 Hz there are 15 data points. However at HF we have excessive resolution - between 4 kHz and 8 kHz there are approximately 800 data points. Simply stated, the longer time window provides good LF resolution, but excessive HF resolution.

Figure 5: The frequency response of the direct sound portion of an impulse response of a 1,250-seat multi-purpose hall. The response was calculated using a 8192 point FFT (which equals a 8192/48000 or ~107 msec). As you can see the frequency response shows low frequency energy that is much more pronounced than seen with the shorter time window.

The result of studying these plots might lead you to conclude that in order to make measurements that correlate well with our listening experience, we must use very short time windows that isolate the direct sound at high frequencies, and increasingly longer time windows as we look at lower frequencies.

At first glance this idea might seem to violate the often quoted phrase, “One can only affect the direct sound with processing.”

However this is not the case. At mid-low and low frequencies, the interaction of a sound system and a room can be affected and optimized by signal processing.

In other words, at low frequencies (long wavelengths) the direct sound and reflections from nearby surfaces combine to form a composite response. It is this composite response that a listener hears.

The ability to measure several time windows simultaneously provides a measurement that both correlates well with human hearing and provides insight into how the signal being sent to the loudspeaker can be tailored (via equalizers, or other processing) to optimize the loudspeaker/room interaction.

Our last figure shows a measurement of a loudspeaker system that includes multiple time windows and displays both the magnitude and phase response of the “system.”

The use of multiple time windows allows one to isolate the direct sound of a loudspeaker in a real-world situation at high frequencies.

However, at lower frequencies, longer time windows that include the loudspeaker/room interaction have been found to correlate well with our listening experience.

Multiple time windows in a single measurement is an extremely interesting way to measure and optimize the response of a sound system in a room.

Sam Berkow has completed a wide variety of acoustical design projects including: concert halls, recording studios, broadcast facilities, production facilities, house of worship facilities, large multi-purpose venues, amphitheaters and stadiums. His educational background includes a masters degree in Engineering from the Stevens Institute of Technology, where he specialized in acoustic measurement and design. He is also the original developer of Smaart acoustic measurement & system optimization software.

David McLain | The Sound System Guy | CCI SOLUTIONS
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Olympia, WA 98507-0481
Voice: 800/426-8664 x255 / Fax: 800/399-8273
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Volume Wars (Part 2)

Personal Monitoring Systems
As mentioned earlier, (IEM’s) In Ear Monitor systems are a saving grace to many in music-audio. They help control the audio monitor levels per individual. Try looking at Aviom products. Each instrument/singer has their own separate audio monitor module as they listen with a pair of headphones or iPod ear pieces. They can separately adjust the overall monitor mix to their liking. This ability gives them the option to pull up or down certain channels as well as their own. The nice part, all the stage volume is gone and everyone can hear themselves without sacrificing the main mix. The IEM signals are routed back to the main board. Guitar players can still use their amps as they are routed through the IEM in their personal channel. Check out Aviom for a more detailed description of their IEM system. Other sound proofing applications are found in drum shields and acoustic tiling.

Better IEMs
Looking for a more interactive monitoring/media/digital/all-in-one stand, while providing more bang for your buck? Try SamePage. Without buying a lincoln-log-set of components, SamePage has a new device that is synced to a personal laptop and networked between other touch-screen displays. From one screen, you can have your own visual monitor mix and digital sheet music display. You can upload, view, save and edit PDF music charts. SamePage, a service and product that was developed for worship leaders by worship leaders, is the world’s only fully integrated software and hardware solution that provides a paperless music management and display. The system allows worship leaders to access their music database, build playlists, view music electronically and download online content right from the stage. SamePage eliminates finding, sorting, organizing, and managing music for each musician and singer by consolidating everything into one system. All stations are linked together allowing the leader to keep the team on the Same Page.

Getting Back to Basics
Is there a way to balance a band without a sound system, IEM and even an engineer? Yes. How? By the band learning how to control their instrument and learn how listen to each other as a unit. Now you're talking about the hard work. Good old elbow grease of teamwork will never be obsolete. Back 20-30+ years ago in garages across America, bands had only 1-2 amps and acoustics. Each player adjusted their volume just enough to hear the entire band and singer. They practiced in this manner. They learned how to balance their sound. They rehearsed the sound of their songs rather than just the songs themselves. The result was a clean and polished compliment to their music. As time, technology and styles of music progressed, the volume levels increased. When sophisticated sound systems arrived, the volume wars spiked. This eventually crept into the Church, and is now where we find ourselves today. The whole genesis of a sound system is not to amplify the band. The real purpose is to make what happens on stage audible.

The time you spend working the sound of your band will have a beneficial result. Never underestimate the power of time well spent. Your band is priceless. Your team will grow musically as well as the quality of your sound. Plus, you help your engineer and audio team to do what they do best - actually mix the music. Instead of pulling down volumes or muting channels, their time can be better spent in adding EQ’s, effects and shaping the range of the sound. All of these details are necessary for the congregation to participate in praise. The worship is well facilitated by a conducive environment. When was the last time that you actually focused in worship without being distracted by noise (both by technology and emotions)?

Branon Dempsey is the Editor-at-Large for PraiseCharts Live as well as the Director and Founder of Worship Team Training: a ministry for local church worship ministries. He has studied and been trained by members of Maranatha! Music and Integrity Music for worship ministry and composition. Branon lives in Cypress, Texas where he is also a Worship Leader/Songwriter and has been in ministry for more than 17 years. Follow him online at © Copyright 2010 PraiseCharts. All rights reserved. Reprinted by permission.

Volume Wars (Part 1)

by Branon Dempsey

Last week, I conducted a small poll on the Worship Team Training site regarding Decibel Levels. 70% of churches rated their volume at 90-95db range. 20% of other houses of worship rated theirs as being 95-100db range, while only 10% remained at 85db’s.

A new book I’m reading is on the spectrum of audio signals for live and studio applications. There were several issues that address volume concerns. One of them was a study conducted over a few years involving studio/album recordings. Sound engineers determine that master volume levels were drastically lower 5 and 10 years ago. Master volume settings for CD recordings use to be at 0.0; now, 5 years later we are pushing anywhere between 2.0 and 5.0 db levels above the historical norm. Now keep in mind, we are not talking about live sound yet. We are discussing what happens in the studio and in the headphones. In the studio world, bands and artists each push the envelope to have the loudest album. Think about your favorite MP3’s. Try this exercise. Listen to any 2008 recording, then pop in something from 2003. You will notice a huge volume drop between the two recordings. You’ll need to boost the volume up a few notches on the 2003 recording just to equal it’s predecessor. Here’s the point. As our ears become more accustom to louder music each year, we turn everything else up to keep our hearing relative. Just think about all the volume levels around you: neighborhoods, traffic, malls, offices and other public places. I’m pretty sure that the music in your church is at least as loud as the noise outdoors. In fact, I bet your sound is 5-10 points higher than it was 10 years ago. For some, this may be a very shy estimate.

The rate of volume changes due to adding instruments, amplification and technology on the stage (and behind the board). We have more toys in our live gear set-up than what we really need. Ok instrumentalists, guitar players and drummers, raise your hands if you like it loud? Uh, huh... Singers, how many of you like it loud? I thought so. The band wins; go figure. Instrumentalist like louder volumes every-time. However, we failed to ask the most important group in our sanctuaries: the congregation. I know I enjoy a good loud thump of the bass and drums along with the roar of guitars. Some may enjoy having the earth moved in their worship centers. To others, this could be an annoyance and could result in people leaving worship services (and the worship leader/team asks why.) Who is the priority? Do we satisfy our artistic needs, or do we facilitate the needs of others for worship? Most of all, are we honoring the Lord through serving each other?There is a purposeful difference between a Friday night gig and a Sunday morning worship service.

War of the Band
About six weeks ago, I was confronted by a worship leader who told me that he had trouble asking his lead guitar player to turn it down. The guitar player was truly gifted, attended all rehearsals, but he showed little respect to his worship leader. As the story goes, the guitarist was persistent in turning up his stage amp, although, the leader repeatedly asked him to turn it down. The worship leader tried several attempts to work with the guitarist as well as to visit with him personally. Upon one evening at practice, the guitarist was asked to turn it down again. The player got up, packed his things and stormed off.

The worship leader asked me what to do. My response: let him go. The last thing that your team and congregation needs is contention and a prima-donna. I shared my personal concern: there are too many players/singers that believe worship/music cannot continue without them. The truth is, God is not dependent our ability to praise Him. In fact, God’s greatness precedes HImself. It is by grace from Holy God that we are called into relationship with Him and a privilege to worship Him. Isaiah puts it this way: “All of us have become like one who is unclean, and all our righteous acts are like filthy rags; we all shrivel up like a leaf, and like the wind our sins sweep us away,” (Isa. 64:6). I don’t think God is calling for any band auditions here. It truly is a unique and humble invitation (not a right) by God to minister to him through music, while leading others into His worship. There’s the key - His worship - not our worship. When we mix our personal griefs/agendas/etc. and the music goal of the team, we are heading for a train wreck. Our real goal: to exhibit Christ-like leadership in being used by the Spirit to facilitate the worship of God. I know this may sound seminarian, but this really is the ultimate truth. At least, this is what we can apply from the words of Paul when he says:

Do not think of yourself more highly than you ought, but rather think of yourself with sober judgment, in accordance with the measure of faith God has given you. Just as each of us has one body with many members, and these members do not all have the same function, so in Christ we who are many form one body, and each member belongs to all the others. - Romans 12:4-5.

The Volume Wars Rage
Now from the spiritual application we move to how this relates to our logistics. When our volumes are out of control, it definitely makes the sound engineer’s job more difficult and frustrating. Like you, I have seen my fare share of arguments between the stage participants and the audio team. Guitarists and drummers get upset because they can’t/want to hear themselves, while the engineers are trying to balance the main mix. Ok, I am going to side with both here. Guitar players get a different feel for the sound and vibe as their levels are up. Especially in working with tube amps, when the tubes are working hard, the tone is dynamically sweeter. When the tubes are idle (or running low) the guitars have no life and impact in the sound. This explains the frustration of the guitarist, as well as the engineer. Can the two really co-exist? Yes, but getting them on the same planet is another struggle. Again, the resolve is to make the right choice based on priority for the greater good. There is a technical solution: IEM’s, which we will dive into in a moment. At all costs, we need to avoid the volume control fighting and train wrecks. This should never happen especially in a service. However, truth be told, I have witnessed a non-verbal volume argument in a service. This is a horrible situation and has no place before the Lord in worship. The service of worship is no place to make a point. If so, we have lost our understanding of worship and our place as being the people of God.

Here’s one instance of how volume wars begin. When the guitar amps are cranked-up on stage, the drummer can’t hear so he plays louder. The bass begins to lose focus on his instrument while they turn up their levels as well. The keyboardist and acoustic guitar is about to pull their hair out and they follow. Everyone else and the vocals become non-existent. At this point, the engineer has lost total control. They can literally mute all the channels on the board and the stage volume takes over the entire room. Ok, let’s understand exactly the job of the engineer. He/she is not a volume control baby sitter. The engineers are just as important as the band in leading worship. They provide shape and dynamic contour of the overall mix. The engineer’s split job is to make sound audible (not amplified) for the congregation; also, they are to assist the band in providing good monitor support. Two of my best sound engineers, Brad Duray (about) and Dan Yeaney (about), told me that their #1 job as an audio team is to be invisible. In fact, Dan went on to say, if there were no negative comments made by a congregation/staff member after a service, then the audio team did their job (in most normal cases). In this scenario, the band’s job is to maintain a good level of stage dynamic, while controlling their instrument and playing volume.

It is true, that if musician has (or develops) a good ear, they can successfully manage their individual volume control. Even more so, they will gain a more polished approach over their instrument and maximize their playing ability. With this adjustment alone, you have solidified one section of your mix. In the event that your entire team makes this adjustment as well, your stage mix will improve by 80%. Result? Two outstanding rewards: (1.) The engineers can actually mix and enhance the sound. (2.) The congregation can sense a balance, hear the singers, and most importantly, they can hear themselves. Volume must be shared by all.

Branon Dempsey is the Editor-at-Large for PraiseCharts Live as well as the Director and Founder of Worship Team Training: a ministry for local church worship ministries. He has studied and been trained by members of Maranatha! Music and Integrity Music for worship ministry and composition. Branon lives in Cypress, Texas where he is also a Worship Leader/Songwriter and has been in ministry for more than 17 years. Follow him online at © Copyright 2010 PraiseCharts. All rights reserved. Reprinted by permission.