Mindblown: a blog about philosophy.

Standing‐wave phenomena are observed in many situations in acoustics and the vibration of strings and elastic structures. Thus they are of interest with almost all musical instruments (both wind and stringed) (see Part XIV in the Encyclopedia of Acoustics [19]); in architectural spaces such as auditoria and reverberation rooms; in volumes such as automobile and aircraft cabins;…

The sound radiation from plates and cylinders in bending (flexural) vibration is discussed in Refs. [9, 27] and chapter 10 in the Handbook of Acoustics [1]. There are interesting phenomena observed with free‐bending waves. Unlike sound waves, these are dispersive and travel faster at higher frequency. The bending‐wave speed is cb = (ωκcl)1/2, where κ is the radius of gyration h/(12)1/2 for a rectangular…

If we are situated in the reverberant field, we may show from Eq. (3.78) that the noise level reduction, ΔL, achieved by increasing the sound absorption is (3.81) (3.82) Then A = S  is sometimes known as the absorption area, m2 (sabins). This may be assumed to be the area of perfect absorbing material, m2 (like the area of a perfect open window…

The critical distance rc (or sometimes called the reverberation radius) is defined as the distance from the sound source where the direct field and reverberant field contributions to p2rms are equal: (3.79) thus, (3.80) Figure 3.23 gives a plot of Eq. (3.78) (the so‐called room equation).

If we have a diffuse sound field (the same sound energy at any point in the room) and the field is also reverberant (the sound waves may come from any direction, with equal probability), then the sound intensity striking the wall of the room is found by integrating the plane wave intensity over all angles θ, 0 < θ < 90°. This involves a…

In a reverberant space, the reverberation time TR is normally defined to be the time for the sound pressure level to drop by 60 dB when the sound source is cut off (see Figure 3.20). Different reverberation times are desired for different types of spaces (see Figure 3.21). The Sabine formula is often used, TR = T60 (for 60 dB): where V is room volume (m3), c is the…

The sound absorption coefficient α of sound‐absorbing materials (curtains, drapes, carpets, clothes, fiberglass, acoustical foams, etc.), is defined as (3.73) Note that α also depends on the angle of incidence. The absorption coefficient of materials depends on frequency as well. Thicker materials absorb more sound energy (particularly important at low frequency). See Figure 3.19. If all the sound energy is…

In a confined space there will be reflections, and far from the source the reflections will dominate. We call this reflection‐dominated region the reverberant field. The region where reflections are unimportant and where a doubling of distance results in a sound pressure drop of 6 dB is called the free or direct field (see Figure 3.18).

Near to a source, we call the sound field, the near acoustic field. Far from the source, we call the field the far acoustic field. The extent of the near field depends on: In the near field of a source, the sound pressure and particle velocity tend to be very nearly out of phase (≈90°). In the far field, the sound pressure…

In enclosed spaces the wave acoustics approach is useful, particularly if the enclosed volume is small and simple in shape and the boundary conditions are well defined. In the case of rigid walls of simple geometry, the wave equation is used, and after the applicable boundary conditions are applied, the solutions for the natural (eigen)…