Helical springs have vast applications in mechanical and electromechanical systems, e. g. shock absorbing and shock isolating constructions, mechanical filters and delay lines. It is, therefore, of fundamental importance to understand the wave propagation along a helical spring. Yoshimura and Murata  investigated the propagation characteristics on an infinite helical spring, which was analitically treated but with the approximation of zero helix angle, though they mentioned the effect of the helix angle. The assumption of zero helix angle decouples the longitudinal motion of the spring from the torsional motion with respect to the axis of the coil. The purpose of the present paper is to investigate the wave propagation along an infinite helical spring with a helix angle, and to see its influence on the phase velocities and the displacement characteristics based on the complete set of the equations. The characteristic equation developed in terms of the frequency parameter shows six possible waves. The propagation velocities at different frequency parameters are numerically computed for the helix angle α=0゜, 5゜ and 10゜ with the ratio of the coil radius to the rod radius R_r=10. The dispersion curves are shown in Figs. 2(α=0゜), 3(α=5゜) and 4(α=10゜). The relative displacements B, V^- and W^- are also shown in Tables 1(α=0. 5゜), 2(α=5゜) and 3(α=10゜). Small value of α(=0. 5) is chosen for this case, instead of α=0, because V^- and W^- are separated or uncoupled when α is zero. The relative displacements indicate the nature of the vibration and the degree of the coupling. Refering to  we may calculate from the static deformation, the normalized propagation velocities of the longitudinal and the torsional motion at zero frequency, that is, C_<pt>=0. 043 and C_<pt>=0. 05 for the zero helix angle when R_r=10. They are indicated in Fig. 2, and fairly meet the two higher velocities. From the relative displacements we find that these two velocities in the lower frequency range correspond to the torsional and the longitudinal motion of the spring. However this distinction of torsional and longitudinal nature is completely lost at the frequency parameter √<K>=0. 342 and √<K>=0. 308, where the half wavelength equals to the circumference of the coil. This is consistent with the fact that Kagawa's result  for finite springs showed no transmission beyond these frequencies. Since Kagawa was paying attention only to the torsional and the longitudinal waves, the absence of these waves in a distinct manner must be interpreted as non-transmission in his case. When α is not zero, the above two kinds of modes are not independent at all but are coupled. As seen from Fig. 3 and 4, the higher two branches of velocities in the lower frequency range are shifted from the static ones. when the helix angle is small (α=0. 5゜) as in Table 1 (K=0. 03), V^-/W^- =-4. 81×10^<-2> for C_p=4. 75×10^<-2> while V^-/W^- =26. 1 for C_p=4. 121×10^<-2>. The first case is predominently torsional and the second case predominently longitudinal where the coupling between both modes is small. For α=5゜ in Table 2, however, we can not say that the vibration is predominently torsional for the first case. This tendency is more pronounced for larger α. Except higher two branches of velocity in the lower frequency range discussed above, most modes are involves with the bending of the rod coupling with the torsion. Some modes in the figures are inclined at about 45゜degrees throughout the frequency range. That is, the propagation velocities are almost proportional to the frequency. There are also some other modes whose velocities are not much effected by frequency. It is seen from the figures and the tables that these two type of modes are coupled, at a certain frequency parameter around ��<K>=1.
The experimental research on the acoustical property of Japanese bell subjected to local loading is presented. The objective of this research is to find the method adjusting the frequency of beat and the duration of remaining tone. Two Japanese bells, so called "Hansho", are used, the one is commercial one and the other is specially made without any character and figure on the surface of the bell. The measurement is carried out as follows; the bell is set in resonance by means of a vibrator controlled by oscillator, and the vibration of the bell is detected by two pick-ups, the one is directly connected to a dual syncroscope and the other through a frequency counter to the same syncroscope. The nodal lines can be determined by comparing the phase difference of the two signals. The natural frequency of the bell is measured by the frequency counter connected to the in-put side of the syncroscope. The frequency of beat and the half life of the remaining tone are obtained from the oscillogram of the bell sound recorded on sound tape. The load is applied in the following way; 1) equally distant four points below the so called "Koma-no-Tsume" hoof, especially, on the H nodal line, L one, and intermediate one of the fundamental tone, 2) a point moving on the circle of the hoof, 3) fifteen points on the bell surface, especially, on the H nodal line, L one, and intermediate one of the fundamental tone. The loading mass is varied from 50g to 200g. The following results are obtained. 1) In general, the natural frequency is lowered by loading the bell. The fundamental tone is affected by loading to the lower part of the bell, and the over tones by loading to the upper part. 2) When the loading is applied on the H nodal line (or L) of the fundamental tone, the L frequency (or H) varies remarkably larger than the H one (or L). Consequently, the beat frequency, that is, the difference between the H and L frequencies, can be controlled. 3) The character and figure scribed on the bell surface seems to affect the over tones, but hardly the fundamental one. In addition, the thinner is the wall of the hoof, the stronger the bell vibrates. 4) The above behavior takes place clearly in case of bell without charactar and figure.
Difficulty in speaking when a single echo is presented to the speaker has been described in a previous paper. We have continued the study on the difficulty in speaking in reverberant sound, using the same technique of simulated sound field. When two or more echoes are presented to a speaker, these echoes have two interesting influences on the criterion of difficulty in speaking. One is the precedence effect in which categories of "no difficulty in speaking" are extended by a preceding echo about 5 dB below the result of single echo, and other is the backward masking effect in that these categories are extinguished by a following echo of a level about 5 dB above the result of single echo. (Fig. 1, Fig. 2, Fig. 3, and Fig. 4) Favorable condition for "speaking" in a sound field composed of reflected and reverberant sound is 10 log(E_1+E_r)/E_t=-20〜-5dB where E_1, E_r and E_t are intensity of reflected sound, of reverberant sound, and talker's level, respectively. (Fig. 5 and Fig. 6) On the other hand, it has been confirmed that difficulty in speaking in an actual multi-purpose hall, for which the results are shown in Fig. 9, agrees with the results obtained by simulation method. It has been made clear in the previous paper, that %-disturbance can be substituted for the difficulty in speaking in the case of single echo, and it is confirmed by comparing Fig. 9 with Fig. 10. that the fact holds in actual reverberant sound field. These results are useful in designing room acoustics and public address system with particular attention to the sound field around the performer.