Abstract
There are some relationships between the various shapes in a Japanese Buddhist temple bell made of cupper-tin, bronze-alloy. These compositions have been inherited since ancient times. This report is focused on the bell made in the period from 14th century to 20th century. The corresponding acoustic characteristics are clarified mainly by Fast Fourier Transformation analysis, which is an efficient algorithm to compute the discrete Fourier transform and its inverse, and the decay time of sound is measured. All this report belongs to Fukushima Prefectural Culture Foundation, Fukushima Cultural Property Centre, Shirakawa branch.
Keywords: Temple bell, Acoustic characteristics, Fast Fourier Transformation.
1. Introduction
Basis of sound
Acoustic characteristic is interdisciplinary science that deals with the study of sound, ultrasound, and infrared sound.
What is sound? Sound is created when something vibrates setting up small fluctuations in air pressure. These fluctuations by sound waves, if they are steady and regular, they will be perceived as tones when they hit the ear drum and pass though the aural chain to the brain. These fluctuations are transmitted in gases, liquids, and solids. The values of some parameters in speed of sound, density, elastic module, and acoustic impedance are given in Table 1. The speed of sound is equal to the square root of the value, Elastic module (Pa) divided by density (kg/m³). The material has the faster of speed of sound, the more effective in acoustic point. The acoustic impedance of a material is defined as the parameter of its speed of sound and density. Acoustic impedance is a ratio of acoustic pressure to and important in the determination of acoustic transmission and reflection at the boundary of two materials having different acoustic impedances and assessing absorption of sound in a medium. This value is the higher, the nicer sound they have in general.
| Table 1. Values of some parameters in speed of sound, density, elastic module, and acoustic impedance |
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Properties of sound waves
Sound waves are characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction. Frequency is the number of times per second that the object vibrates, referred to as Hertz (Hz). Such a theory as lighter and harder to bend is better for acoustic material has been considered in the past. It means that the value of E (elastic module) / r (density) is the higher, the better for acoustic material. The values of main metals in elastic coefficient and density are given in Table 2.
| Table 2. Values of main metals in elastic coefficient and density |
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Sound pressure over the frequency spectrum
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The perception of loudness is a strong function of the frequency of sound. The human auditory system is sensitive to frequencies from
20 Hz to a maximum of around 20,000 Hz, although the hearing range decreases with age. Sensitivity of ear is non-linear with respect
to frequencies in audio range. Maximum perceived loudness occurs near 4 kHz; sound pressure levels which are just detectable at 4 kHz
are not detectable at other frequencies. In general, two tones of equal power but different frequency will not sound equally loud.
The baby’s cry and the lady’s scream are considered to the highest sensitivity and close to 4 kHz (Figure 1). These features are fundamental factors to assess acoustic characteristics and they are observed and appeared to influence the degree and quality of the sound, bronze bell. |
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2. Experiment
The restored temple iron bell is hit by rubber hammer (300 g) and wood hammer (500 g). Hammers and bell is given in Figure 2.
Measurement point
The rectangular axis of the axis of blowing direction is 0°, and then that axis is turned 45° and 90°. The sound is measured on those axes 0.5 m apart from the temple bell (Figure 3). In general the direction of 0° and 90° does not have the beat but the one of 45° has beat in the basic sound of temple bell (constituent of lowest frequency). Therefore two measurement points make possible to observe the phenomenon of beat clearly.
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| Figure 2. Temple bell and two hammers (left: rubber hammer, right: wood hammer) |
Figure 3. Measurement point |
Measurement system
To observe the constituent of frequencies and sound decay time the measurement system of Figure 4 is used.
The measurement object of sound is recorded by MD (Mini Disc) recorder and then data is compressed in order to record as long as possible. Some kinds of object sound are influenced by compressed signal but it has been proved by some experiments that as far as temple bell’ sound, the sound is composed by separated spectrum and does not affect by compressing.
The frequency of object sound is analyzed by FFT (Fast Fourier Transformation) of PC system with the recording sound by MD recorder.
The decay sound time is analyzed by Noise measurement with 1/3 octave band analysis. Electronic signal is sent to noise measurement and record decay characteristic of 1/3 octave band sound pressure level with memory function. These characteristics are achieved to calculate the time of the sound pressure decay of 60 dB, sound decay time.
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Figure 4. Measurement system |
3. Results and discussion
Sound frequency
The frequency of partial sound is as following.
Basic sound 384.05 Hz
Sound of second part 992.55 Hz
Sound of third part 1878.1 Hz .
The example of frequency analysis is given in Figure 5. First graph is the wave of sound pressure. Vertical axis sound pressure (Pa) and horizontal axis is time (second, record for 10 seconds). Second graph is spectrum graph. Vertical axis is frequency (Hz, maximum 4000 Hz) and horizontal axis is time (second, record for 10 seconds). The hue of color is the strength of sound. Third graph is the result of FFT analysis. Vertical is relative spectrum level (dB, range of analysis 50 dB) and horizontal axis is frequency (Hz, maximum 4000 Hz).
The sound of this temple bell is that sound of second part is dominant but after 5 seconds it disappeared and basic sound left for longer time. The sound of third part stayed only 1 second.
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| Figure 5. Example of frequency analysis |
Sound decay time
This iron bell sound is fewer spectrums compared to bronze bell sound but decay time is longer, it means that lingering sound is longer and sound is more beautiful (Figure 6).
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| Figure 6. With wood hammer, 90°, 0.5 m (left top), with wood
hammer, 45°, 0.5 m (right top), with rubber hammer, 90°, 0.5 m (right below), with rubber hammer, 45°, 0.5 m (left below) |
Following temple bells are in order to compare acoustic characteristic (Figure 7).
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| Figure 7. Examples of temple bell |
Bronze used for making Japanese temple bells is essentially an alloy of copper and tin from the ancient to now. The shape, thickness, and the edge thickness are unique and they are different from Chinese and European bell. Tin are used from 13 to 15 % in Japanese bell. Before 1868 it is considered that tin are used around 7 % and the edge thickness is thicker than nowadays. So the characteristic of these bells is that sound decay time is shorter. Iron bells are very difficult to achieve the ideal Japanese bell sounds.
4. Conclusion
It is possible for iron bells to make same sound as bronze bells but frequency of up sound has big difference between iron bells and bronze bell. It means that it is impossible to make similar sound. Model experiment suggests that if following points are considered,
it would be possible for iron to make more similar sound as bronze.
- The thickness should be thinner in order to have same frequency of basic sound in the same shape as bronze.
- If the thickness is thinner as a whole, the frequency up sound would be strong and shrill. In order to control that situation, the upper
part of bell should be thicker than bronze bell.
- Fundamentally it is impossible to make same sounds but it should be considered in order not to lose the sound of meditation.
Acknowledgement
All these experimental data belongs to Fukushima Prefectural Culture Foundation, Fukushima Cultural Property Centre, Shirakawa branch and Tsunenobu Okuma.
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* Paper of the 4th International Conference ArtCast 2008: Casting, from Rigor of Technique to Art, May 2008
University Dunarea de Jos of Galati - Faculty of Metallurgy and Materials Science, Galati, Romania
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