## 1 Introduction  
The rapidly increasing number of vehicles is in the world, especially in many developing countries, has raised the serious problem of traffic noise [1; 2; 3]. Traffic noise is disturbing to the daily routine of residents along the roads [4]. Many issues, physiological [5] and psychological [6] health problems, are demonstrated to be related to a noisy environment. To reduce traffic noise, one of the most effective methods is to set noise barriers along the roads [7].  
Current research on noise barriers primarily focuses on noise calculation [8; 9], the effects of barrier shapes [10; 11], and the design of barriers [12; 13; 14; 15]. As one of the important aspects, prediction of the insertion loss by the noise barrier has been attracting the attention of scholars, and both mathematical and experimental approaches have been developed. The mathematical formula was first developed by [PERSON] in 1896 [16] and has been subsequently developed by many other scholars. As such, rigorous diffraction results can be calculated in mathematical methods, e.g., the Boundary Element Method [17], the Finite Element Method (FEM) [18], and the Finite Difference Method (FDM) [19]. In many cases, the typical procedure for the mathematical computation is too complicated to be applicable to the engineering application. Alternatively, comprehensive sets of data have been measured to plot the experimental attenuation of noise barrier since 1940 [20]. The most famous data set is the Maekawa chart [21], and many experimental formulae were developed based on [PERSON]'s original chart [22; 23], including [PERSON] and [PERSON]'s derived formula [24]. [PERSON] and [PERSON]'s formula is widely used and is regarded as the simplest experimental practice for application in China and many other countries. Fresnel number, which is the single parameter in [PERSON] and [PERSON]'s diffraction formulae, is the ratio between the path length difference and half of the sound wavelength [25; 26].  
In practical application, the path length difference of a noise barrier is defined by a particular source-barrier-receiver geometry and easily measured. However, because of the multiple frequency components of traffic noise, the computation of diffraction is always time consuming. The noise frequency changes according to the different types of vehicles travelling at various speeds. Hence, the noise protection performance of the barrier depends on the traffic flow states. For simplicity, an equivalent frequency of 550 Hz can be set to represent the total frequency band in the calculation of diffraction suggested in the FHWA traffic noise model [27]. In the 1/3 rd-octave-band spectrum, the frequency of 500 Hz is used in the approximate calculation of diffraction and noise reduction effect of a sound barrier [9; 28; 29; 30; 31]. However, the data used was collected from 1993 and 1995, and the characteristics of vehicle noise have changed since then because of the variety of vehicle types and speeds [32]. Moreover, in the micro traffic noise prediction model, the reduction effect of a noise barrier should consider every vehicle to be point source. Therefore, a single 500 Hz frequency is not adequate in the noise reduction calculation of a sound barrier.  
In this paper, data of the noise spectrum of different vehicles in a variety of speed ranges were measured to calculate the equivalent frequency. The corresponding relationships among vehicle type, speed, and noise frequency were obtained. Several path length differences were preset to calculate the 1/3 rd-octave-band diffraction and the total diffraction. Next, verification experiments were established to ensure the calculation accuracy of barrier diffraction based on different equivalent frequencies. Last, an application of the approach to different traffic flows is implemented, and the effects of a barrier to traffic noise for different speeds and different types of constituents are analyzed.