## 1 Introduction  
The problem of noise has drawn widespread attention and has been the subject of studies in recent years [1; 2; 3]. Centrifugal pumps are extensively applied in many fields related to the national economy [4; 5]. During the operation of pumps, due to the periodic rotation of rotating parts, the flow inside the pumps and the interference between impeller and volute are both repetitive, and cause periodic pressure fluctuations in the flow field, consequently, repetitive impulsive noise [6] is generated. The noise generated by centrifugal pumps can affect human health, degrade the pump flow performance, consume extra external energy and depreciate the working environment [7]. As the regulations for environmental noise become increasingly strict, methods that lower the noise are becoming more significant. Therefore, it is crucial to have a better understanding of radiation noise frequency characteristics, to provide theoretical guidance for research on radiation noise prediction and control technology at different frequencies of centrifugal pumps. In the past, considerable research has been carried out in terms of the frequency characteristics of centrifugal pump noise. [PERSON] and [PERSON] [8; 9] experimentally analyzed the dynamic pressure pulsations spectrum at the pump discharge site, and summarized that the blade-passing excitation amplitude is the highest amplitude in the pressure spectrum. [PERSON] et al. (2010) analyzed the inner sound field in low frequency ranges and reported that the inner sound field could be characterized by a dipole-like source located near the tongue. [PERSON] et al. (2011) found that the blade-passing frequency (BPF) and its harmonic frequencies are the main frequencies of the flow noise in pipelines and the sound pressure level (SPL) at BPF is higher than the others. [PERSON] et al. (2012) reported that the SPL at BPF reached a peak value near the solute tongue. As is known, centrifugal pumps always work in various conditions with various working demands, [PERSON] (2013) concluded that the change of flow rate had a great influence on flow noise, especially on the SPL at BPF. Using the near field acoustic pressure method, [PERSON] et al. (2014) measured radiation noise under various flow rate conditions, and discovered that the SPLs with a high frequency of 1000 and 2000 Hz made a significant contribution to the overall A-weighted sound pressure level. With the development of computational fluid dynamics (CFD) technology, numerical calculation methods have been widely adopted by scholars (15; 16). A hybrid method combining CFD with Lighthill acoustic analogy has been widely used to elucidate and predict acoustic generation (17; 18; 19). [PERSON] et al. (2010); 21 applied it for noise calculation in a two-dimensional centrifugal pump and concluded that the main noise source was the dipole source. The dipole source was defined as an unsteady fluid force acting on the wall surface, including the impeller dipole source and the solute dipole source in centrifugal pumps. The impeller-generated radiation noise at BPF exhibited obvious dipole characteristic behavior (22), while the solute-generated radiation noise clearly showed asymmetric directivity characteristics, i.e., the radiation noise in the direction facing the tongue was higher than that in the direction against the tongue (23). [PERSON] et al. (2014) also validated the important impact of the pump cavity dipole source on calculation results. In addition, the pump structure modal response was considered to obtain more accurate results, [PERSON] et al. (2015) studied the effect of different structures on SPL at BPF and provided guidance for structural optimization of centrifugal pumps. Obviously, radiation noise has direct impacts on living and working environments. According to the above literature review, previous experimental research has mainly focused on the internal flow noise characteristics in centrifugal pump pipes, while little experimental research has focused on radiation noise outside the pumps.