close to the source so that we are in the near acoustic field, not the far acoustic field. However, if appreciable reflections or background noise (i.e. other sound sources) are present, then we must measure the intensity Ir in Eq. (3.41). Figure 3.8 shows two different enclosing surfaces that can be used to determine the sound power of a source. The sound intensity In must always be measured perpendicular (or normal) to the enclosing surfaces used. Measurements are normally made with a two‐microphone probe (see Ref. [22]). The most common microphone arrangement is the face‐to‐face model (see Figure 3.9).
The microphone arrangement shown also indicates the microphone separation distance, Δr, needed for the intensity calculations [22]. In the face‐to‐face arrangement a solid cylindrical spacer is often put between the two microphones to improve the performance.
Figure 3.8 Sound intensity In, being measured on (a) segment dS of an imaginary hemispherical enclosure surface and (b) an elemental area dS of a rectangular enclosure surface surrounding a source having a sound power W.
Figure 3.9 Sound intensity probe microphone arrangement commonly used.
Example 3.8
By making measurements around a source (an engine exhaust pipe) it is found that it is largely omnidirectional at low frequency (in the range of 50–200 Hz). If the measured sound pressure level on a spherical surface 10 m from the source is 60 dB at 100 Hz, which is equivalent to a mean‐square sound pressure p2rms of (20 × 10−3)2 (Pa)2, what is the sound power in watts at 100 Hz frequency?
Solution
Assuming that ρ = 1.21 kg/m3 and c = 343 m/s, so ρc = 415 ≈ 400 rayls:
then from Eq. (3.47):
Example 3.9
If the sound intensity level, measured using a sound intensity probe at the same frequency, as in Example 3.8, but at 1 m from the exhaust exit, is 80 dB (which is equivalent to 0.0001 W/m2), what is the sound power of the exhaust source at this frequency?
Solution
From Eq. (3.41)
Sound intensity measurements do and should give the same result as sound pressure measurements made in a free field.
Far away from omnidirectional sound sources, provided there is no background noise and reflections can be ignored:
(3.49)
and by taking 10 log throughout this equation
(3.50)
where Lp is the sound pressure level, LW is the source sound power level, and r is the distance, in metres, from the source center. (Note we have assumed here that ρc = 415 ≅400 rayls.) If ρc ≅ 400 rayls (kg/m2s), then since I = p2rms/ρc
So,
(3.51)
3.8 Sound Sources Above a Rigid Hard Surface
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 power level of the source and r is the distance in metres.
Figure 3.10 Source above a rigid surface.
In this discussion we have assumed that the sound source radiates the same sound intensity in all directions; that is, it is omnidirectional. If the source of sound power W becomes directional, the mean square sound pressure in Eqs. (3.48) and (3.46) will vary with direction, and the sound power W can only be obtained from Eqs. (3.41) and (3.47) by measuring either the mean‐square pressure (p2rms) all over
