CUADERNOS DE ARQUITECTURA Y URBANISMO.

The measurement procedure for a volume diffuser is in principal the same as the method outlined above, though with additional receiver angles as shown in Figure 2.2. The procedure adopted was broadly as follows.

Scattered pressure distributions were measured in a semi-anechoic chamber following the procedure outlined in Section 2.5.1. The lower cut-off frequency for the room, determined by the depth of the wall mounted foam, was approximately 250Hz. The samples were fixed into a central 600mm×600mm sample plate that slotted into a fake floor, comprising a series of plywood boards connected by tongue and groove edges. These were unvarnished, though were of a high quality finish, and were assumed to be acoustically rigid. This was replaced with a flat board of the same dimensions for background measurements. Receivers were placed in a circle of radius r = 1.35m from the centre of the array, with an angular step of 9° starting from θ = 0°. An MLS signal (of length 213-1 = 8191 samples) was produced by a source located a distance of r0 = 2.5m from the array centre. Figure 2.11 shows the

measurement setup for an array of aluminium cylinders of 1m in height, arranged according to an optimised sequence introduced in Chapter 6 and shown later in Figure 2.27.

Due to the rectangular shape of the room the angle of incidence was restricted to -30° ≤ θ0 ≤ +30°, though by using source angles of θ0 = {30,0,30} and rotating the

square sample board through steps of 90°, all angles of incidence in angular steps of 30° are effectively allowed, starting from θ0 = 0°. All distances were restricted by the maximum

dimensions of the room, which for the samples measured resulted in a characteristic distance,

rc ≈ 1.75m. This meant that in order for approximate far-field conditions to be met, as given in

Section 2.2.3, measurements were normally carried out at either 1:3 or 1:4 scale. For the intended frequency range (after scaling) of 400Hz-4kHz, this meant that for higher frequencies the far-field conditions as defined by Eqs. 2.3-2.4 were not possible, which for the samples used corresponded to cut-off frequencies (when scaled) of approximately 1.7kHz, 4.0kHz, and 1.0kHz for the 1:1, 1:3 and 1:4 scale models respectively. Using the criterion of no more than 20% of receivers in the specular zone however resulted in a maximum diffuser size, Dmax, of approximately 410mm. Whilst for diffusers of this size the start of potential

Chapter 2: Prediction and measurement

44

near-field behaviour may be observed at higher frequencies, as the main purpose of the measurement was to validate the prediction models, this was deemed acceptable.

Figure 2.11: Semi-anechoic measurement setup both with (top) and without (bottom) a 2D planar volume diffuser as per Figure 2.27 constructed at 1:4 scale (source off bottom of shot)

45

The measurement equipment used was as follows:

 Source –Visaton 50mm diameter SC-4-ND-4Ω tweeter loudspeaker.

 Receivers – 40 custom-made Bridge 3/16” diameter piezoelectric microphones.

 Acquisition unit – 01dB NetdB PRO-121 and NetdB PRO-132 12 channel and 32 channel real time analysers respectively, in chain mode for synchronous acquisition of 40 channels at sampling frequency, fs = 51.2kHz.

To allow comparison between real world measurements and the 2D prediction models used each scattered pressure result is converted to a normalised scattered pressure, ps,norm, which

unless otherwise stated shall be assumed in all scattered pressure plots throughout. This was achieved using the following method. Both measured and modelled results were divided by that of the incident pressure at a reference receiver, pi,ref, taken from the background

measurement. This eliminates the influence of source strength and the frequency dependent magnitude of the 2D model. The reference was taken to be the back receiver, that is θ = θ0+180°, which has the advantage that during measurements the source will always be

on-axis to the rear receiver, ensuring that the high frequency directionality of the transducers is not an issue. In addition for the reference receiver used, scaling factors of r_c /2and rc/2

may then be applied to the 2D model and 3D measurement results respectively, where the characteristic distance rc is defined by Eq. 2.3. This removes the effects of cylindrical and

spherical spreading respectively to account for difference in behaviour due to distances used in the setup.

For convenience, throughout the rest of the chapter it is assumed that where sample and background measurements are referred to all measurements have been deconvolved with their appropriate loudspeaker-microphone response, as described in Section 2.5.1. For reference, the average loudspeaker-microphone response from the 40 microphones used during the measurements is shown in Figure 2.12. Ideally this response would be flat across the measurement bandwidth, though this is clearly not the case. It would be expected that frequencies below approximately 1.0-1.5kHz (unscaled) may suffer from a low signal-to-noise ratio, which is due primarily to the response of the tweeter.

Chapter 2: Prediction and measurement 46

500

1000

2000

4000

8000

16000

55

60

65

70

75

80

85

90

95

100

Frequency, f (Hz)

L

ouds

pe

ake

r-

m

ic

rophone

r

es

pons

e (

dB

/V

)

Mean

Mean  2

Figure 2.12: Average loudspeaker-microphone response used during the polar measurement for the 40 microphone setup shown in Figure 2.11

In addition to the low frequency limitations of the system, Figure 2.12 displays two further points at which there are potential signal-to-noise ratio / discontinuity problems. These frequency regions are centred on approximately:

 3.0kHz (unscaled) – corresponds to the point at which approximately half a wavelength is equal to the source diameter. This may have been due to a zeroth order structural resonance.

 13.5kHz (unscaled) – equates to the point at which sound radiating from the back and diffracting around the tweeter is out of phase with the sound propagating from the front. This was largely unavoidable since sealing the back of the tweeter would lead to a very low level output, whilst the use of any baffle / sealed enclosure on the tweeter may introduce unwanted reflections into the space.

47