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

Similarity Principle and its Acoustical Verification Lintao Liu α , Guocheng Wang σ , Huiwen Hu ρ , Cong Shen Ѡ , Zhonghua Li ¥ , Zhimin Shi § , Yu Xiao χ , Xuepeng Sun ν , Heng Sun Ѳ & Yanji Yao ζ Abstract- This study finds a similarity principle: the waves emanated from the same source are similar, as long as two wave receivers are close enough. The closer the wave receivers are, the more similar the received waves are. We define the similarity mathematically and verify the similarity principle by acoustical experiments. I. I ntroduction man has two ears (acoustical receivers), which are not very close. When a cicada is singing, the two ears should hear high similar sounds, which makes the man feel that there is only one cicada singing. When many cicadas are singing, the two ears should listen to low similar sounds, which makes the man think that there are many cicadas singing. An interesting question is: what will happen if the distance between two ears becomes shorter or longer? Gravitational waves have been observed at two stations (H and L stations) ( 1,2 ) . Our studies (unpublished) show that gravitational waves received at two stations are highly similar. Such high similarity can verify the existence of the gravitational wave and the uniqueness of the gravitational wave origin. One should note that the distance between gravitational wave receivers (though several thousand miles) is very short compared to the remote distance of gravitational wave propagation. When dealing with the seismic wave data (recorded by one seismometer) caused by the two consecutive big blasts at Tianjin China in 2015, we found that the time-frequency similarity of the two seismic waves reached 96% ( 3 ) . Such a similarity is high enough to make us sure that, only according to the seismic wave data, the two blasts took place at the same site even though the equivalent magnitudes of the two blasts are several times different. Here, we emphasize that high similarity can help us verify the uniqueness of wave origin. So, one can imagine: would low similarity means the multi-origin of waves? Our answer to this question is nearly positive, concluded by the acoustical experiments in this study. The waves, such as acoustical, electromagnetic, seismic, and gravitational ones, if emanated from the same source, might show similarity to some degree, no matter what the wave transmission medium is. This study will show that the similarity varies with the distance between two wave receivers. In Section 2, a similarity principle is given. Section 3 defines the similarity function mathematically. We verify the similarity principle by the acoustical experiments in Section 4. Finally, we will have some discussions. II. S imilarity P rinciple 1. The waves emanated from the same source are similar, as long as two wave receivers are close enough. The closer the receivers are, the more similar the received waves are. 2. When a proper distance between the wave receivers is fixed, the high similarity of received waves means a unique origin of the waves. In contrast, the low similarity means multi-origins of the waves. III. M athematical D efinition of S imilarity There are many ways to measure the similarity of two variables ( 4, 5 ) . Most reflect the degree of linearity, like the Pearson correlation coefficient (6) , where a high value figured out means the two variables are linear while a low value means nonlinear. Based on the condition, we will choose a suitable measurement to calculate the similarity ( 7 ) . The similarity is a tool, by which we can research kinds of scientific problems. In the principal component analysis, the principal component can be extracted by the correlation coefficient which could be regarded as similarity (8) . The similarity can be used to analyze two images for spatial concordance (9) , and also used in Complex Network Graphs (10) . Here, similarity refers to the degree of limit correlation of the concerned oscillating information in two time data sets, and its value interval is [−1,1] . The similarity makes it feasible to estimate the time delay between the two datasets. If the two datasets are not disturbed by noise, then the similarity is determined by a formula similar to the correlation coefficient’s, by which the corresponding delay estimation can be worked out directly. Generally, assuming that there are two closely separated observation stations, respectively recording the infinite oscillation time datasets 1 ( ) ∈ and 2 ( ) ∈ , the similarity between the oscillating A © 2022 Global Journals Volume XXII Issue III Version I 51 ( ) Global Journal of Human Social Science - Year 2022 B Corresponding Author α: State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences; Wuhan 430077, China. e-mail: llt@asch.whigg.ac.cn Author σ ¥ χ ν ζ : State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences; Wuhan 430077, China. Author ρ Ѡ § Ѳ : University of Chinese Academy of Science; Beijing 100049, China.