VRIJE UNIVERSITEIT BRUSSEL Acoustics - the Dept. of ...

52 CHAPTER 3. MEASURING SOUNDderivative of p is :∂p∂x = p mkcos(kx) = kp m (3.7)The approximation p A −p B is given by :p A −p BrThe relative error equals := p m(sin(kr/2)−sin(−kr/2))re = p mk −2p m sin(kr/2)/rp m k= 2p msin(kr/2)r= 1− 2sin(kr/2)kr(3.8)(3.9)Example : suppose one uses an intensity meter wit a 6mm spacer to measurethe intensity at 12kHz. It can be calculated that k = 217.9m −1 and thereforekr/2 = 0.65 and e = 0.07. The relative can be seen to equal 7%. This errorwill increase rapidly when using a bigger spacer.3.10 Measuring sound sources3.10.1 Measurements in an anechoic half-spaceAn anechoic half-space is a room that is confined (usually at the bottom)by a hard surface, that reflects the sound waves (see Figure 3.16). Along allother walls there is in principle no material border, or, the sound waves arecompletely absorbed (and not reflected). This anechoic half-space is realisedoutside on a hard concrete surface (without buildings or other objects inthe near surroundings), or inside in an acoustical dead room with a hardfloor. The measurements of the sound power in an anechoic half-space areconducted as described in the ISO standard 3745 [4]. The sound source isplaced on the hard surface. The measuring points, n in number (6 or 8)are placed at a distance far enough from the source to guarantee that themeasurements areconducted inthefarfield(seeFigure3.16). Inpracticethismeans that the measuring points are placed at a distance of at least threewavelengths from the source. Moreover the measuring points spaced outover the half-space (on a half spherical surface) in such a fashion that everypoint is concerned with an equal part of the surface S i . This means that :nS i = 2πr 2 . If the machine radiates non-omnidirectional sound, the variousmicrophones will not measure equal sound pressure. One will therefore takeinto account the ’spatial average effective’ pressure p p in the expression ofthe power W :W = I2πr 2with I = p2 mρc(3.10)