# Research Progress on Curved Plates in China: Applications in Architecture
## 3 Acoustic Characteristics of Curved Plates
### Principle of Surface Acoustic Design  
Due to the different properties of sound waves at different scales, the propagation properties of acoustic waves should be considered when discussing the acoustic characteristics of curved plates. From the law of sound propagation in air, it can be seen that the wavelength is longer at low frequencies. Between 4 m and 5 m, waves show obvious diffraction characteristics when passing through some small-scale building elements or furniture (such as columns and chairs) and obvious reflection and diffusion characteristics when passing through large walls or floors [58]. At medium and high frequencies, the wavelength is short, which can produce diffusion and reflection effects on the surfaces of tiny elements. Since building elements have little influence on sound when sound waves diffract, this discussion will focus specifically on reflection and diffusion characteristics [58]. However, curved plates have a great influence on the sound propagation path due to their geometric characteristics. On the same scale, using the characteristics of reflection and diffusion mentioned above [58], curved plates can be embodied as concave sound aggregation and convex sound diffusion in practical applications, with both applications presenting greater advantages than those of flat plates [59]. Therefore, when it is necessary to plan and adjust the sound path, curved plates may be a good choice. The reflection of a sound source in a room mainly has three conditions: plane reflection, concave reflection, and convex reflection. As shown in Figure 2a, plane reflection can produce a certain degree of diffusion, while a convex surface forms a more obvious diffusion [59]. Full diffusion in the hall can distribute sound energy uniformity, smoothly improving the full interior sound field distribution of reverberation time attenuation, to ensure an appropriate early decay time, decrease the difference in sound level between the front and rear rows, and adjust the balance of clarity and fullness. It can also eliminate the possibility of quality defects, such as echoes and sound focusing acoustic, and suppress the acoustic feedback, which is very beneficial to improve the sound quality of the hall. This effect is widely used in architectural acoustics. A concave surface produces sound focusing, which will form the virtual sound source S' under certain circumstances. Energy is concentrated near the virtual sound source, resulting in insufficient sound pressure at a distance and resulting in uneven sound energy density in the hall, thereby affecting the audio-visual experience. This situation should be avoided as much as possible in practical applications. However, sound focusing, to a certain extent, can compensate for the problem of insufficient sound pressure in the back of an auditorium and improve the sound energy density in the back seating area by using sound focusing to balance the sound field of the entire auditorium [60]. When a curved surface is applied in the acoustic design of theaters, to achieve a certain sound diffusion effect, different geometric shapes can be constructed on the surface of the sidewall, back wall, and ceiling of the theater according to the requirements of interior art, such as a semipillar (triangular, semicylindrical, etc.) and embossed details (Figure 2b,c). Triangles and semicylinders have simple structures and great d  
Figure 2: (**a**) Three basic situations of sound wave reflection indoors. (**b**) Concert hall sound diffuser group [61]. (**c**) Various forms of sound diffusers. Comparison of sound diffusion effects of triangular prism and semicylindrical diffusers: (**d1**) specific structure size, (**d2**) acoustic diffusion of triangular prisms, and (**d3**) acoustic diffusion of a semicylinder, where arrows indicate the direction in which sound waves are projected.