The sound absorption coefficient (α) of trees was theoretically derived and expressed as α=G·f^1/2, where f is frequency and G is a constant; since the value of G cannot be calculated directly, absorption coefficients of four kinds of trees were experimentally measured by the reverberation-chamber method. It was found that sound energy was absorbed mainly by the leaves of trees and not their trunks. The values of G were determined by comparing theoretical and experimental results, and were found to be between 0.001 and 0.002. The attenuation in vegetation was theoretically expressed by G. To check the accuracy of this, experiments were carried out using two kinds of trees. The sound energy absorbed by tree leaves was measured. The theoretical values agreed approximately with experimental results, indicating that the attenuation through absorption can be predicted.

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The frequency response and the Young's modulus, shear modulus and internal friction were measured for square boards with regularly-grained planes in several kinds of wood, which included Sitka spruce for stringed instrument top plates and maple for back plates, and for square boards in an acrylic resin of plastics and an aluminum of metals. The Sitkaspruce was the highest in response frequency, higher in sound power level, the greatest, in level variation and the greatest in level drop with increasing frequencies above 1 kHz, and it had the response pattern of high level in the range of middle frequencies. In contrast, the maple had the response pattern of low and almost flat level as a whole. In order to havesuch frequency responses, it was necessary that wood for top plates had not only the excellent vibrational properties in the direction along grain but also the strong anisotropyin regularly-grained plane, and that wood for back plates had the characteristics opposite to those of wood for top plates.

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This paper investigates the influence of modeling error that is the difference of the characteristic between the secondary path and its model on the behavior of the filtered-X LMS adaptive filter. The equations that describe the behavior of the adaptive filter are presented at first, and the influence of modeling error is considered based on the equations. Both the stability and the noise reduction performance are discussed, and particularly, we discussed in detail the noise reduction performance under modeling error condition that has rarely been considered. In addition, the conditions required for maintaining the noise reduction performance is also presented. The results of the theoretical consideration are confirmed by computer simulation in which the impulse responses measured in a vehicle cabin are used. Through the investigation, it is proved that the algorithm may be stable except for the substantial modeling error case, and the noise reduction performance will be inferior to that under ideal condition in general. These results suggest that we should use the on-line identification system when the secondary path characteristic is time variant.

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For the prediction and control of vibration and structure-borne noise generated by various kinds of machinery and equipment installed in buildings, it is necessary to know the vibromotive force of the machinery. It seems to be necessary to standardize the method for determination of vibromotive force. This method should not only have sufficient accuracy, but also be simple as much as possible and applicable to the field measurements. In order to be fullfilled these requirements, we have put the main point on the development of substitution method, and basic studies on the important subjects of this method were carried out. In this paper, the important results are described.

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