High-resolution measurements of directivity patterns

"Experimental investigation of high-resolution measurements of directivity patterns" Andrea Corcuera Marruffo, Alexander Mayer, Alex Hofmann, Vasileios Chatziioannou, Wilfried Kausel. In proceedings of the 47th Annual Conference on Acoustics  DAGA 2021. 

Link to the paper

Intro

Measuring and modelling the directivity characteristics of sound sources is a long-standing challenge in acoustics that has received increased attention in recent years. Knowing the directional properties of sound sources is important in several applications such as in the design of new auditoriums, virtual sound environments and in the manufacture of musical instruments.

Musical instruments are sound sources that create sound fields with complex directivity patterns which are frequency dependent and may also vary depending on the dynamics. Due to the difficulties in providing an accurate, repeatable excitation, the directivity patterns of musical instruments are often measured for all angles simultaneously using large surrounding spherical microphone arrays. While the use of this method allows measuring the directivity characteristics of an instrument that is excited in a natural manner, the spatial resolution of the measurements is limited by aliasing as a consequence of the spatial sampling strategy. On the other hand, a repeated capture system makes it possible to acquire higher resolution directivity patterns at the expense of obtaining patterns that do not include the influence of a player

Measurement setup

The directional characteristics of a Bb trumpet were measured in the anechoic chamber of the Department of Music Acoustics - Wiener Klangstil, at the University of Music and Performing Arts Vienna (see Figure 1). The trumpet was excited articially using a horn driver (PA horn driver MRD-120) that was attached to the mouthpiece using a custom-made holder. A stepped logarithmic sine sweep from 150 Hz to 10000 Hz was used to measure the directivity signals. The amplitude of the input signal was modied to avoid the saturation of the measurement microphones. The trumpet was mounted on an automated turntable that was rotated by 0.5, from 0 to 360, resulting in a total of 721 measurement points per plane. The measurements were done in three different planes, namely the horizontal, vertical and median planes of the instrument. To this end, the setup was manually modied by rotating the trumpet in order to modify the measured plane. The directivity signals were captured using a microphone that remained static, at a distance of 1 meter. The height of the microphones was determined with a laser pointer targeting the centre of the instrument's bell. Each full rotation took approximately 12.5 hours.

Analysis

The analysis of the signal was done in the time domain. First, the time-domain response signals were delay-compensated. The delay corresponding to the distance of 1 meter was removed, equivalent to 146 samples at 50 kHz sampling rate. Then, the response signals were divided in blocks of 5000 samples (equal to the duration of each frequency point in the stepped sweep), windowed using a Hanning window (L = 5000) and bandpass filtered with a lter whose cut-off  frequency corresponded to the current excitation frequency of the signal. This was done with the aim to guarantee the analysis of steady and clean signals, independent of unwanted influences, like harmonic distortions. Finally, the signals were normalized with respect to the reference signal that was recorded inside the mouthpiece. The normalized data were converted to dB and plotted in a polar plot. Negative levels are articially set to 0 dB for plotting purposes.

Results

Directivity of the trumpet in the horizontal, median, and frontal planes at lower (250, 500, and 1000 Hz) and higher frequencies (2000, 4000, and 8000 Hz)