Category: 3. Sound Generation and Propagation

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…

In most sound fields, sound propagation occurs in two or three dimensions. The three‐dimensional version of Eq. (3.1) in Cartesian coordinates is (3.29) This equation is useful if sound wave propagation in rectangular spaces such as rooms is being considered. However, it is helpful to recast Eq. (3.29) in spherical coordinates if sound propagation from sources of sound in…

If the sound pressures p1 and p2 at a point produced by two independent sources are combined, the mean square pressure is (3.25) where 〈〉t and the overbar indicate the time average . Except for some special cases, such as two pure tones of the same frequency or the sounds from two correlated sound sources, the cross term 2〈p1 p2〉t disappears if T → ∞. Then…

The sound intensity level LI is given by (3.24) where I is the component of the sound intensity in a given direction and Iref = 10−12 W/m2 is the reference sound intensity.

The sound power level of a source, LW, is given by (3.23) where W is the sound power of a source and Wref = 10−12 W is the reference sound power. Some typical sound power levels are given in Figure 3.5.

The sound pressure level Lp is given by (3.22) where pref is the reference pressure, pref = 20 μPa = 0.00002 N/m2 (= 0.0002 μbar) for air. This reference pressure was originally chosen to correspond to the quietest sound (at 1000 Hz) that the average young person can hear. The sound pressure level is often abbreviated as SPL. Figure 3.4 shows some sound pressure levels of typical sounds.

The range of sound pressure magnitudes and sound powers of sources experienced in practice is very large. Thus, logarithmic rather than linear measures are often used for sound pressure and sound power. The most common measure of sound is the decibel. Decibels are also used to measure vibration, which can have a similar large range of…