Livingroom Acoustics

Room Acoustics and Music

For large rooms, auditoria, etc., the classical work on reverberation is based on geometrical concepts. Sound was considered to travel in rays and sound energy to be uniform, not undulant. Predictions of performance in large auditoria based on this approach agreed fairly well with measurement, but when smaller rooms are considered, the effect of resonance may be more significant and greatly affect the energy distribution. Thus for domestic rooms, wave motion must also be considered. Speech utilises only a small area of the auditory area, music considerably more.

Fig 1. Most of the sound reaching an individual in the audience at a concert or show arrives via reflections off the building or its contents. The ratio of direct and reflected sound may depend to some extent on the position of the individual in the auditorium

The acoustic problem of the small enclosure such as a domestic living room is aggravated by the ear's capacity to span ten octaves. If we take the extremes as 20 Hz. and 20 MHz., we find that for a room 8.6m long, there is fundamental resonance at 20 Hz. Thus, at this frequency a standing wave will be set up between the end walls such that the sound pressure will vary from a maximum at the wall surface to zero at the centre of the room.  In these circumstances, it is clearly necessary to approach acoustic problems from the standpoint of standing waves and resonances

At 20 KHz. the wavelength is only about 15mm - small compared to the length of a 8.6m room. While theoretically a standing wave of this length could be maintained over this distance, in practice small irregularities of the wall surfaces would diffuse the sound and destroy the resonant effect. As eardrums and microphone diaphragms are also large in comparison to this wavelength, the effect of standing waves would be still further reduced. Thus at these high frequencies an approach based on ray acoustics is quite suitable. Below about 300 Hz. ray acoustics cease to be of value, and it is only when the low frequency resonances in a small room are adequately controlled in the general interest of sound quality, that the diffusion of sound is sufficient to give reasonable validity to reverberations calculated according to the ray approach.

'Colourations' due to room resonances (normal modes) are often a problem with speech. These may take the form of monotonous emphasis of certain frequencies in a speaker's voice. They may also affect music, but are more difficult to isolate because of the transient nature of musical sound. Also, our hearing is more sensitively attuned to the human voice than to music. Standing waves can accentuate particular notes by as much as 8 or 10dB.

In a room, a mode is heard as a colouration of the desired sound if there is a tendency to reinforcement at the modal frequency. If a certain modal frequency is isolated from its neighbours, it is more likely to be audible. At the higher frequencies (above about 300 Hz) the individual modes are seldom distinguishable, but below this, isolated modes are common and often troublesome.

There is a tendency for faults caused by bad room acoustics to be rejected by the listener's binaural hearing. Some considerable imperfection can therefore be tolerated in the acoustic behaviour of a room. Nevertheless, the extent of this binaural compensation is limited, and it is preferable to reduce the adverse influence of a room to the minimum.

The air enclosed within a room will vibrate in a complex manner. To understand the acoustics of a room fully, it is necessary to understand especially the characteristic frequencies and standing waves associated with it. There are three basic standing wave patterns which can form in a room: axial, tangential and oblique.

If the sound source is located in the south wall of a rectangular room, there are three types of standing wave systems possible. In an axial mode, reflections from one pair of surfaces are involved, the north and south walls. The east and west walls, floor and ceiling are not involved as they lie parallel to the wave path. Tangential waves are distributed parallel to two surfaces, where they are parallel to floor and ceiling, being reflected off all four walls. The third vibratory pattern involves reflections of oblique waves from all six surfaces. The axial modes are of the greatest practical significance in small listening rooms.

It is fortunate that in most small rooms having reasonably absorbent surfaces, only the axial modes are significant. However, the others should not be completely ignored, as they can in some circumstances become intrusive.

resonant mode

Fig 2. A pipe closed at both ends helps us to understand how resonance occurs between two opposite walls of a listening room or studio. The distance between the walls determines the frequency of resonance. Resonance modes occur when the distance between the room's walls equals half the wavelength of the sound, and at multiples of half a wavelength. Notice that there are always sound pressure (volume level) peaks at the walls.

The pipe resonance illustrated in fig. 2 can be likened to one axial mode of a room. There are three such modes in a rectangular enclosure. One of these as already noted involves north and south walls. Others occur similarly between the other walls, and the floor and ceiling. The spacing of these modes determines the degree to which the reproduction of sound is likely to be affected. Above 300 Hz. the modal frequencies of a small room are so close together that they tend to merge harmlessly. However, below about 300 Hz. their separation is greater and it is in this region that problems can arise. Both experiment and mathematical analysis have shown that if a modal frequency is separated from its neighbours by more than approximately 20 Hz. it will tend to be isolated acoustically. It will not be excited by its neighbours or held in control by them. It can, therefore, pick out a component of the signal at its own frequency and give the amplitude of this frequency a large resonant boost, thus colouring the sound.

Let us take for an example a room 8.6m long x 4.9m  wide x 3.1m high. The length resonates at 20Hz. with harmonics at 40, 60, 80, 100, etc. The two side walls 4.9m apart resonate at a frequency of 35Hz. with harmonics at 70, 105, 140,175, etc. Similarly, the floor ceiling combination resonates at 56 Hz. with harmonics at 112,168, 224, 280, etc.  There are 47 of these resonant frequencies below 500 Hz.

The tangential and oblique modes with their harmonics do in fact add to these characteristic frequencies. However, because of the greater path lengths, these modes have lower fundamental frequencies and their amplitude tends to be less because of the increased number of reflections. So, although the total number of modes below 500 Hz., considering all these types of waves, exceeds 1500, most colourations of the sound can be attributed to normal modes.

From table 2, it can be seen that the greatest interval between modes is 20 Hz so, on this basis, the room should be satisfactory. Nevertheless, coincidental modes can be troublesome, and these occur at 140 and 280 Hz. Problems may occur at these frequencies. The separation of these combined modal frequencies is an important criterion in predicting the quality of sound in a room and in understanding problems in existing rooms.

 

Length 8.6m

Width 4.9m

Height 3.1m

fo

Hz

Hz

Hz

1

20

35

56

2

40

70

112

3

60

105

168

4

80

140

224

5

100

175

280

6

120

210

 

7

140

245

8

160

280

9

180

315

10

200

 

11

220

 

12

240

 

13

260

14

280

15

300

Table 1: The fundamental frequencies and harmonies of the three axial modes of a 8.5m x 4.9m x 3m room

All normal modes in ascending order

Differences

between modes

Hz

Hz

20

15

35

5

40

16

56

4

60

10

70

10

80

20

100

5

105

7

112

8

120

20

140

0

140

20

160

8

168

7

175

5

180

20

200

10

210

10

220

4

224

16

240

5

245

15

260

20

280

0

280

0

280

20

300

15

315

Table 2: modal frequencies for a 8.5m x 4.9m x 3m room grouped in ascending order 

In a room without parallel surfaces, difficulties due to standing waves may be reduced. In the upper part of the spectrum there will be increased sound diffusion. Bass frequencies will-however still tend to excite room modes as they are associated more with volume than with shape. If a room's boundaries are arranged so that they diverge at a rate of 1:7 or more, so many normal modes are caused that sound colouration due to the action of an isolated mode is avoided.  However, irregular rooms would fit badly into conventional houses and it would be more fruitful to look at proportion-as a means of controlling room behaviour. If any dimensions of a room are the same or simple multiples of each other, then modal frequencies will coincide with undesirable additive effect. To avoid such coincident modes, preferred proportions derived from, wave acoustics may be employed.

preferred room ratios

Fig 3: Bolt’s Graph of preferred ratios of room dimensions derived mathematically from wave acoustics to distribute modal frequencies in the best way. Points A, B & C are derived from a more recent computer study by Sepmeyer. 


The graph in fig. 3 plots acceptable length to width ratios for unity height. Interestingly most historically held acoustically 'ideal' ratios fall outside this area. This would perhaps suggest that in real situations, ratios outside those calculated offer acceptable results. In using the graph, it is important to note that any point inside the bounded area may be used in calculating dimensions, but dimensions must not be simple multiples of each other.

Ludvig W. Sepmeyer’s more recent study seems to indicate that some points within or near Bolt's area may be superior in distributing modes. Three of these are shown in fig. 3. These proportions do not ensure good room acoustics, but they do optimise the situation, avoiding the worst adverse conditions. Preferred room dimension ratios are:     

A             B             C

Height   1.00        1.00        1.00

Width    1.14        1.28        1.60

Length  1.39        1.54        2.33