Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 102
Solution
ОглавлениеWe know that l = λ/12, λ = 343/150 = 2.29 m, and Wm = 0.1 watt. If we compare the sound power of a dipole Wd with that of a monopole Wm (Eqs. (3.44) and (3.45)) we find that
Therefore, the sound power radiated by the dipole is 9 mW.
In practical situations with real directional sound sources and where background noise and reflections are important, use of Eq. (3.43) becomes difficult and less accurate, and then the sound power is more conveniently determined from Eq. (3.41) with a sound intensity measurement system. See Ref. [22] in this book and chapter 106 in the Handbook of Acoustics [1].
We note that since p/ur = ρc (where ρ = mean air density kg/m3 and c = speed of sound 343 m/s) for a plane wave or sufficiently far from any source, that
where Eq. (3.46) is true for random noise as well as for a single‐frequency sound, known as a pure tone.
Note that for such cases we only need to measure the mean‐square sound pressure with a simple sound level meter (or at least a simple measurement system) to obtain the sound intensity from Eq. (3.46) and then from that the sound power W watts from Eq. (3.41) is
for an omnidirectional source (monopole) with no reflections and no background noise. This result is true for noise signals and pure tones that are produced by omnidirectional sources and in the so‐called far acoustic field.
For the special case of a pure‐tone (single‐frequency) source of sound pressure amplitude, , we note that and from Eq. (3.47).
For measurements on a hemisphere, W = 2πr2 p2rms /ρc and for a pure‐tone source , and , from Eq. (3.47).
Note that in the general case, the source is not omnidirectional, or more importantly, we must often measure quite 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.
