2024-02-20: Spherical speaker measurement

For purposes of sound installations we made a second design for speaker enclosures as a spherical shape for the Faital Pro 4FE32 drivers. The outer diameter of the sphere is 18cm, 3D printed from PLA with 4mm banana plug terminals and holders for a handle and/or mic stand attachment.

The infrastructure used was the following:

• Audio interface: Native Instruments Komplete 6 @ 48 kHz, mic gains at 12h, output volume dial fully clockwise.
• Amplifier: d&B D6 @ Linear preset, -30 dB
• Microphone 1: NTI M2230 + MA220 preamp
• Microphone 2: Sennheiser MKH 8020

The space was our mdw Klangtheater, the loudspeaker and microphone position was at an elevation of 2.17m above the reflective floor. The other walls and ceiling were at a distance of > 5m, walls damped with curtains.

We conducted three measurements in frontal direction with the two microphones at a distance of 1 meter. The enclosure was filled with polyester wool in different amounts:

• Empty speaker enclosure
• Speaker enclosure half-filled
• Speaker enclosure fully filled (not stuffed though)

Excitation was with two different sources:

• Pink noise (Reaper JS Pink Noise generator plugin at 0dB)
• Exponential sine sweep (20-20kHz) at -3dB

The Pink noise plugin's frequency reponse is close to 1/f by ±1dB.

The time window until the first reflection has a length of (sqrt(d**2+4*h**2) - d)/c. For d = 1m and h = 2.17m this amounts to 10 ms.

However, we can see from the impulse response measurements that the actual length is more 8.5 ms. The reason is not completely clear, but it seems we have reduced the height by some 30 cm after measuring because of rattling in the stand we used for the speaker.

After windowing up to the first reflection, the frequency charts show interesting results. The filling amount of the enclosures influences the bass response only marginally, although the volume of the enclosure decreases. Secondly, in the range of 1–3 kHz resonances are efficiently damped. These correspond to the standing waves inside the sphere. See (Rocchesso 2001) for reference where Table 3 lists the frequencies for a sphere of approximately double the size (r=0.188m in the paper compared to r=0.086m in our case). The lowest resonance modes in our case would be: 1331 Hz, 2135 Hz, 2872 Hz, 2887 Hz. Since the net effective radius of the sphere is even smaller because of additional internal structures, this corresponds well to the resonances exhibited in the spectral graphs.

The two microphones compare quite well, with the NTI having a raised mid region compared to the MKH.