Tsukasa Yoshinaga – yoshinaga@me.tut.ac.jp
Hiroshi Yokoyama – h-yokoyama@me.tut.ac.jp
Akiyoshi Iida – iida@me.tut.ac.jp
Toyohashi University of Technology
1-1 Hibarigaoka, Tempaku, Toyohashi 441-8580 Japan

Tetsuro Shoji – tetsuro.shoji@music.yamaha.com
Akira Miki – akira.miki@music.yamaha.com
Yamaha Corporation
10-1 Nakazawacho, Nakaku, Hamamatsu 430-8650 Japan

Popular version of paper 2aMU1 Numerical investigation of effects of lip stiffness on reed oscillation in a single-reed instrument
Presented 9:35-9:50 morning, June 9, 2021
180^th ASA Meeting, Acoustics in Focus

Single-reed instruments, like clarinet, produce sounds with reed vibrations induced by airflow and pressure in the player’s mouth. This reed vibration is also affected by the sound propagation in the instrument so that the player can change the musical tones by controlling the tone holes. Therefore, to analyze the single-reed instrument, it is important to consider the interactions among the reed vibration, sound propagation, and airflow in the instrument. In particular, the airflow passing through a gap between the reed tip and mouthpiece becomes turbulent, and it has been difficult to investigate the details of the interactions in the single-reed instruments.

In this study, we conducted a numerical simulation of sound generation in a single-reed instrument called Saxonett which has a clarinet mouthpiece and recorder-like straight resonator.  In the simulation, airflow and sound generation were predicted by solving the compressible Navier-Stokes equations, while the reed vibration was predicted by calculating the one-dimensional beam equation. To accurately predict the turbulent flow in the mouthpiece, computational grids were needed to be smaller than the turbulent vortices in the airflow (approximately 160 million grid points were constructed). In contrast, the simulation time became larger than the usual flow simulation because the frequency of musical tone was relatively low (approximately 150 Hz). Therefore, the supercomputer was needed to simulate the turbulent flow and sound generation associated with the reed vibration.

By setting a mouth-like pressure chamber around the mouthpiece in the simulation and inserting the airflow, the reed started vibrating and the sound was produced from the instrument. Moreover, amplitudes of the reed oscillation as well as the sound generation were changed by adding the lip force on the reed. Then, by controlling the lip force, a stable reed vibration was achieved. As a result, the reed waveform and sound propagated from the instrument well agreed with the experimental measurements.

With this simulation technology, we could observe the details of airflow and acoustic characteristics inside the instrument while the player is playing the single-reed instrument. By applying the simulation to various designs of the instruments, we can clarify how the sound is produced differently in each model and contribute to the improvement of the sound quality as well as the player’s feeling.

Numerical simulation of the single-reed instrument. Blue to red color shows the pressure amplitude whereas the rainbow color vectors indicate the flow velocity.

Mark Rau – mrau@ccrma.stanford.edu
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
660 Lomita Court
Stanford, California 94305, USA

Popular version of paper ‘1aMU2’ Measurements and Analysis of Acoustic Guitars During Various Stages of Their Construction
Presented Tuesday morning 9:50 – 10:05am, June 08, 2021
180^th ASA Meeting, Acoustics in Focus

Stringed instruments have an internal structure which determines how they vibrate and produce sound when driven by the strings. This internal structure is made up of multiple vibrational resonances and is referred to as the resonant structure. Many stringed instrument builders (luthiers) will take acoustic measurements of instruments as they are being built to probe the resonant structure and make changes so that the instrument will sound as intended. However, the resonant structure of the instrument continuously evolves throughout the construction process, so it is unclear at which stage the acoustic measurements should be made.

To address this, we measured the resonant structure of three guitars during their construction. Two guitars are of the Orchestra Model (OM) style and were made by the Santa Cruz Guitar Company. The third is an 000-28 style guitar built by the author. The guitars were measured at multiple stages while being constructed, including: during the bracing of the top, construction of the box, sanding, application of polish, and once fully constructed. The stages of construction of the 000-28 are shown in Figure 2.

Figure 1: The three guitars in their completed state. The left and center guitars are the OMs and the right guitar is the 000-28.

Figure 2: Various stages of the 000-28 construction.

The resonant structure was measured by using a small hammer to impart a force to the instrument, and a laser Doppler vibrometer to measure the resulting vibrations. This provided the frequency and amplitude of each structural resonance as well as how long it would ring once struck.

Figure 3: Vibration measurement setup.

The lowest resonances are the most important, because they fall near the fundamental frequencies of most notes on the guitar, so we tracked how the first three prominent resonances changed. Figure 4 shows the frequency response of the 000-28 with the box constructed and sanded (top right of Fig. 2) and the guitar fully constructed (bottom right of Fig. 2). The lowest three prominent resonances are circled and their structural mode shapes are shown for the guitar box.

Figure 4: Frequency response of the 000-28 box (left) and completed guitar (right). The lowest three prominent resonances are highlighted.

We observed some general trends as the guitar evolves, such as the resonant frequencies and amplitudes decreasing as the guitar nears completion, particularly as the polish is applied. If one is trying to achieve a specific sonic quality from an instrument, we recommend taking measurements before the final sanding and adjusting the amount of sanding based on these observations. Final alterations can be made by carving the braces through the sound hole.

Kyota Nomizu – k-nomizu@chiba-u.jp
Sho Otsuka – otsuka.s@chiba-u.jp
Seiji Nakagawa – s-nakagawa@chiba-u.jp
Chiba University
1-33 Yayoi-cho, Inage-ku
Chiba-shi, 263-8522, Japan

Popular version of paper 2aMU5
Presented Wednesday morning, June 9, 2021
180^th ASA Meeting, Acoustics in Focus

A tuning fork is a metal device that emits a sound of a certain frequency when struck. Tuning forks are used for various purposes, such as music, medicine, and healing. In addition to the fundamental frequency component, the harmonic tone appears immediately after struck, with a 6-times higher frequency. First of all, the accuracy of the fundamental frequency is needed. Additionally, the fundamental tone needs to be sustained for a long time, while the harmonic tone should decay rapidly. However, only the fundamental frequency is tuned in the manufacturing process of the tuning forks, durations of tones have not been evaluated. In addition, most studies on tuning forks have been about frequencies of tones or mode analysis, and those on the vibration duration are very limited.

Figure 1: Tuning forks used in the experiment.

In this study, we aimed to assess individual differences in the vibration duration of tuning forks. Also, we tried to clarify factors that affect the vibration duration. In this study, as a first step, we evaluated the effect of the holding force.

In the experiment, we struck four individual tuning forks of the same type and recorded their sound, and estimated durations of their fundamental and harmonic tones. Measurements were repeated with changing the holding force.

Figure 2: Evaluation of the vibration duration.

As a result, significant individual differences in the duration of fundamental and harmonic tones were observed. Especially, the tuning fork with the shorter length and the smaller mass had a shorter fundamental tone. Also, the duration of fundamental and harmonic tones varied depending on the holding force. The best holding forces for both tones were different for each tuning fork.

These results suggest that even for the same type of tuning fork, small differences in shape and heterogeneity of the material may affect the vibration duration. It is also suggested that there is a desirable holding force for each tuning fork that can achieve both a long duration of the fundamental tone and rapid decay of the harmonic tone.

Figure 3: Duration of the fundamental tone at each holding force range.

In the future, based on these results showing the relationship with the holding force, it is necessary to conduct a comprehensive study on the effects of shape parameters and environmental conditions such as temperature and humidity. It is thought that the results theoretically contribute to improving the manufacturing process of tuning forks, which currently relies on the empirical knowledge of artisans.