Acoustics and sound propagation: Part 4

Sound refraction occurs whenever a sound wave passes from one material to another of differing density. So it will occur as a sound wave moves from air into a sound absorber, for example, but it can also happen within the same material if its density changes. Most solids are pretty stable in this respect, of course, but the density of the air itself is constantly changing, particularly in terms of heat and humidity, and so sound waves can change direction quite noticeably. This can be a serious issue for outdoor live sound systems (and sometimes even for indoor systems in large arenas, where the heat of the audience can affect the sound propagation significantly). It’s not impossible for audience areas that received good sound during soundchecks to receive almost nothing when the audience has been in situ for a while, as the warmer, less dense air around the audience causes the sound waves to refract away from their intended destination! Temperature changes when the sun sets, or when there’s a breeze in the air, can cause similar propagation problems.

As the signal frequency is increased further the level heard at the hole will fall again until the signal frequency reaches twice that of the original resonance, whereupon another modal resonance or standing wave will occur, boosting the level again. In this case, there are pressure maxima at both ends and in the centre, with two nulls at the quarter-length points — and again the sound energy reflected from the sealed end exactly aligns with the direct sound, causing the energy to build up and reinforce itself. This modal resonance process continues at all the multiples of the original frequency: 3f, 4f, 5f and so on.

This concept lies at the heart of most musical instruments, of course, from organ pipes and woodwind through to all the various stringed instruments. Reducing the effective length of a string by trapping it between finger and fretboard changes the frequency at which it resonates, as does uncovering holes in a wind instrument or changing the length of tubing in a brass instrument.

But while modal resonances are an essential part of making music, they also cause problems when trying to listen to it! In an enclosed space — a room of some kind — any sound waves will normally reflect off the walls, floor and ceiling. The spacing of opposite walls (front/back, left/right, floor/ceiling) will determine their individual resonant frequencies. At some frequency (and its multiples) sound-wave reflections between opposite surfaces will self-reinforce, resulting in a modal resonance or standing wave. If the room was a perfect cube then all three dimensions would support exactly the same resonant frequencies, and if you placed your head in the exact centre of the room at the lowest resonant frequency you would hear nothing at all. At twice the frequency you would hear a huge boost in energy, and at three times the frequency it would all go very quiet again! But move a few feet up and to one side and you’ll find you can hear sounds that were previously absent, and the previously loud frequencies aren’t anything like as loud.

Given the size and construction of typical rooms, modal resonances normally only occur strongly for frequencies below about 250Hz, but it can be a very frustrating problem if you are trying to listen critically to music, with some bass notes booming and others almost absent. The problem can be minimised by designing the room so that the three primary dimensions are all different and non multiples of each other, which helps to spread out the modal resonances in the different dimensions. Efficient low-frequency absorption is then the most commonly used solution to try to prevent the reflections from building up in the first place — but it takes a lot of absorber to make a significant difference below 100Hz. Again, wavelengths come in to play here as the absorber needs to be deep enough to affect the long-wavelength, low-frequency wave fronts. Careful placement of speakers and listening positions, to ensure they are not sited in nodes, is also very important — and sometimes moving a speaker or the listening position a few inches can make an enormous difference to the quality and consistency of sound.

These kinds of modal problems don’t just affect the artificial reproduction of sound, of course. It can affect mic placement and even the placement of instruments themselves, too, as the instrument behaves much like a loudspeaker and the mic much like the ear. In practice, it’s likely only to affect bass instruments (or amplifiers) such as bass guitars, double basses and kick drums, and then only in relatively small environments, such as a stage alcove. But if you find the sound unexpectedly boomy or thin on certain notes think about moving the instrument and/or mic further away from the walls!

Different microphones have different polar patterns, and consequently capture more or less of the diffuse sound environment. To capture a good balance of direct to reverberant or diffuse sound, an omnidirectional microphone has to be placed no more than 30 percent of the room’s critical distance from the source. So if the room’s Dc is three metres, an omnidirectional mic should be placed no more than about one metre from the source. Clearly, in close miking situations that is easily achieved, but it can become more of an issue in an orchestral recording, for example. A cardioid mic, which rejects a lot of rearward sound, can be placed up to 50 percent of the Dc from the source (1.5 metres in this example) while still capturing an acceptable balance of direct and reverberant sound. If it is necessary to place the microphone further away, then the critical distance must be increased by installing sound absorbers or reducing the reverberation through other means. There are no other options! In a large live-sound venue, don’t forget that the audience can act as a very efficient sound absorber, and the Dc will increase dramatically in a full venue compared to an empty one!  0