Every divided time interval shorter than 500ms in two experiments is presented by three sound bursts. The length of divided interval is remarkably overestimated to the length of empty interval when the divider is far from both the markers and the divided interval comes before the empty variable interval. Under such a condition, discontinuously high values of PSE appear, which shows the effect of subjective dividing. Rated dividing ratio comes always nearer to 1/2 than physical dividing ratio, and the trend is stronger when the divided interval is physically shorter. The following hypothesis can explain our data: (1) The subjective length of a subjectively divided time interval is equal to the sum of the subjective lengths of all the parts. (2) The subjective length of a subjectively empty time interval is in proportion to the sum of its physical length and a constant(≑80ms).
The sound pressure distribution of standing waves and the attenuation characteristics of plane waves in a straight tube with a solid end are derived as a function of attenuation constant δ, using the fundamental equation which holds for plane waves propagating in a tube with frictional dissipation. Calculated results of the acoustic characteristics are given as a function of the non-dimensional attenuation coefficient η, which is fixed by the attenuation constant δ times length of tube l. The attenuation constant δ are measured by using these acoustic characteristics of plane waves in a straight tube with frictional dissipation. The experimental results of attenuation constants δ regress to the approximate equation, which is derived from a fundamental equation. The calculated values of attenuation constant δ by regression formula are compared with the experimental results, and they are found to be in good agreement. From these results, the following facts are confirmed that the attenuation constant δ is given as a function of a sound wave length and Reynolds number which is fixed by the inner diameter of a tube, kinematic viscosity and the sound velocity, and that the attenuation constant δ can not be negligible for the acoustic characteristics of resonance frequency ranges in a tube system.
The exhaust systems such as used for automotive internal combustion engines can be replaced by the four terminal constants (A, B, C and D) of an electrical equivalent circuit as their whole silencing systems. The four terminal matrices for the cases of straight tubes and branched ones in the typical tube systems are derived by considering the attenuation constant δ of plane waves in a tube. It also includes the four terminal matrices of the plane waves propagating without any losses in a tube. The general equation for insertion loss of silencing systems having expansion chamber type muffler are derived by these four terminal matrices. Calculated results of the insertion loss by these equation are compared with the experimental results of pure sound tests, and they are found to be in good agreement. From these results, it is confirmed that the insertion loss in the resonance frequency ranges of a silencing system is numerically calculated by the four terminal matrices considering the attenuation constant δ of plane waves propagating in a tube with dissipation caused by wall friction.