Mindblown: a blog about philosophy.

There are three main modeling approaches in acoustics, which may be termed wave acoustics, ray acoustics, and energy acoustics. So far in this chapter we have mostly used the wave acoustics approach in which the acoustical quantities are completely defined as functions of space and time. This approach is practical in certain cases where the…

For a homogeneous plane sound wave at normal incidence on a fluid medium of different characteristic impedance ρc, both reflected and transmitted waves are formed (see Figure 3.13). From energy considerations (provided no losses occur at the boundary) the sum of the reflected intensity Ir and transmitted intensity It equals the incident intensity Ii: (3.64) and dividing throughout by Ii, (3.65) where R is the energy…

Sometimes noise sources are distributed more like idealized line sources. Examples include the sound radiated from a long pipe containing fluid flow or the sound radiated by a stream of vehicles on a highway. If sound sources are distributed continuously along a straight line and the sources are radiating sound independently, so that the sound power/unit…

The directivity index DI is just a logarithmic version of the directivity factor Q. It is expressed in decibels. A directivity index DIθ,ϕ may be defined, where (3.59) (3.60) Note if the source power remains the same when it is put on a hard rigid infinite surface Q(θ, ϕ) = 2 and DI(θ, ϕ) = 3 dB. EXAMPLE 3.11 SOLUTION

In general, a directivity factor Qθ,ϕ may be defined as the ratio of the radial intensity 〈Iθ, ϕ〉t (at angles θ and ϕ and distance r from the source) to the radial intensity 〈Is〉t at the same distance r radiated from an omnidirectional source of the same total sound power (Figure 3.12). Thus (3.53) For a directional source, the mean square sound pressure measured at distance r and angles θ and ϕ is p2rms (θ,ϕ). In…

The sound intensity radiated by a dipole is seen to depend on cos2 θ (see Figure 3.11). Most real sources of sound become directional at high frequency, although some are almost omnidirectional at low frequency. This phenomenon depends on the source dimension, d, which must be small in size compared with a wavelength λ, so d/λ ≪ 1 for them to behave almost…

In practice many real engineering sources (such as machines and vehicles) are mounted or situated on hard reflecting ground and concrete surfaces. If we can assume that the source of sound power W radiates only to a half‐space solid angle 2π, and no power is absorbed by the hard surface (Figure 3.10), then (3.52) where LW is the sound…

3.7.1 Sound Power of Idealized Sound Sources The sound power W of a sound source is given by integrating the intensity over any imaginary closed surface S surrounding the source (see Figure 3.7): (3.41) The normal component of the intensity In must be measured in a direction perpendicular to the elemental area dS. If a spherical surface, whose center coincides with the source,…

The radial particle velocity in a nondirectional spherically spreading sound field is given by Euler’s equation as (3.37) and substituting Eqs. (3.34) and (3.37) into (3.15) and then using Eq. (3.35) and time averaging gives the magnitude of the radial sound intensity in such a field as (3.38) the same result as for a plane wave. The sound intensity decreases with the inverse…

The second term on the right of Eq. (3.33), as before, represents sound waves traveling inward to the origin and is of little practical interest. However, the first term represents simple harmonic waves of angular frequency ω traveling outward from the origin, and this may be rewritten as [4] (3.34) where Q is termed the strength of an omnidirectional (monopole) source situated at the…