Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 137
Solution
ОглавлениеTable 3.3 gives all the possible natural frequencies for modes under 100 Hz using Eq. (3.94) and c = 343 m/s.
One can see in Table 3.3 that the frequency spacing becomes smaller with increasing frequency and that there may be degenerate modes present (i.e. when two or more modes have the same characteristic frequency but different values of nx, ny, and nz). Modes which are close to each other in frequency can easily “beat,” while degenerate modes can greatly increase the response of the room at particular frequencies where degeneracy occurs. This can give rise to the “boomy” sensation (at low frequencies) which is often found in regular‐shaped rooms of similar wall dimensions [4].
Table 3.3 Frequencies (less than 100 Hz) for a 3.1 × 4.7 × 6.2 m3 rectangular room, for c = 343 m/s.
| n x | n y | n z | f E |
|---|---|---|---|
| 0 | 0 | 1 | 27.7 |
| 0 | 1 | 0 | 36.5 |
| 0 | 1 | 1 | 45.8 |
| 0 | 0 | 2 | } 55.3 |
| 1 | 0 | 0 | |
| 1 | 0 | 1 | 61.9 |
| 0 | 1 | 2 | } 66.3 |
| 1 | 1 | 0 | |
| 1 | 1 | 1 | 71.8 |
| 0 | 2 | 0 | 73.0 |
| 1 | 0 | 2 | 78.2 |
| 0 | 2 | 1 | 78.0 |
| 0 | 0 | 3 | 83.0 |
| 1 | 1 | 2 | 86.3 |
| 0 | 1 | 3 | 90.7 |
| 0 | 2 | 2 | } 91.6 |
| 1 | 2 | 0 | |
| 1 | 2 | 1 | 95.7 |
| 1 | 0 | 3 | 99.7 |
The position of the sound source within the room is also an important parameter, since for many source positions certain types of modes may not be excited. For example, if the source is located in one of the corners of the room, then it is possible to excite every normal mode, while if the source is located at the center of a rectangular room then only the even modes (one eighth of the total number of possible modes) can be excited. Similarly if we keep the position of the source constant and measure the sound pressure throughout the room we see differences in level depending on where we are standing in the room relative to the normal modes. In this way the room superimposes its own acoustical response characteristics upon those of the source. Hence we cannot measure the true frequency response of a sound source (e.g. loudspeaker) in a reverberant room because of the effect of the modal response of the room. This interference can be removed by making all the wall surfaces highly sound‐absorbent. Then all the modes are sufficiently damped so we are able to measure the true output of the source [4]. Such rooms are called anechoic (see Figure 3.22).
