Global Journal of Human-Social Science, B: Geography, Environmental Science and Disaster Management, Volume 22 Issue 3

information in the two datasets can be measured by the following equation. (1) This function is called the similarity function, where D represents an integral time period, showing the length of the information concerned; D+l means the period D translates rightly by l time; s denotes the delay time index; denotes a time interval. We call (2) as Similarity Coefficient between the concerned oscillating information around l time, if (3) Here, ′ can be regarded as the delay of the oscillating information in 2 ( ) to that in 1 ( ) . The similarity coefficient takes the positive value when the oscillating information is positive phase correlated, and it takes the negative value when the oscillating information is reverse-phase correlated. If time series 1 ( ) ∈ and 2 ( ) ∈ are disturbed by noises, the similarity function (1) can be substituted by ( 11 ) (4) where denotes a normal time - frequency transform (NTFT) ( 12, 13 ) , in which and denote time and frequency respectively; Re denotes the real part. S denotes the time-frequency area concerned; S+l denotes area S translating rightly by l time. IV. A coustical E xperiments To verify the above similarity principle, two acoustical experiments have been done in our work. The first experiment is one sound source test, and the other three sound sources test. We use two microphones to receive the sounds. In each experiment, a series of distances (0.008m, 0.2m, 0.415m, 1.5m, and 4.3m.) between two microphones have been set, reflecting how the Similarity Coefficient varies with the distance. Every recording time series lasts about 30 seconds with a sampling frequency 128KHz. Figure 1: The Similarity Coefficient in Two Experiments Fig.1 shows the result of the two experiments. Each line shows the Similarity Coefficient varies over the distance between two microphones. In fact, the Similarity Coefficient is averaged along the time. The red line corresponds to one source and the blue line to three sources. Figure 1 shows that the Similarity Coefficient decreases with the increasing distance based on the red line. The blue line shows some difference in this phenomenon. When the distance is close, its trend is the same compared to the red line. When the distance is far, the Similarity Coefficient shows a little increase. We conjecture it may be caused by the position distribution of two microphones and three sources, which requires further research. However, despite the close or far distance between two microphones, the Similarity Coefficient is larger than 0.9 in an enough close distance (it can be 0.008m in our experiments). On the contrary, less than 0.3 in a far distance (4.3m). It can be concluded that if the distance between two microphones is not close enough, the Similarity Coefficient is down sharply. The two acoustical experiments are sufficient to verify Similarity Principle Ⅰ that the closer distance between the two receivers, the higher similarity of the two received waves. Volume XXII Issue III Version I 52 ( ) Global Journal of Human Social Science - Year 2022 © 2022 Global Journals B Similarity Principle and its Acoustical Verification ρ ,( ) = + ∫ 1 ( ) 2 +( ) + ∫ 1 2 ( ) + ∫ 2 2 +( ) ∈ , ∈Δ γ( ) = ρ , ' ( ) ∆ ρ , ' ( ) | | = ρ ,( ) | | ( ) ρ ,( ) = ∬ + Ψ 1 τ,ϖ( ) ( ) Ψ 2 τ+ ,ϖ ( ) ( ) τ ϖ ∬ + 2 Ψ 1 τ,ϖ( ) ( ) τ ϖ∬ + 2 Ψ 2 τ+ ,ϖ ( ) ( ) τ ϖ ∈ , ∈Δ Ψ τ ϖ