# Historical Church Bell Tower Structural Behavior Induced by [PERSON]'s Acoustic Wave Propagation
## 2 Materials and Methods
### Acoustic Wave Source Recording  
In this study, the mechanical pressure signal of the seven bells is considered as the primary forcing vibration source, used as input by the dynamic simulation software to reproduce the expected vibroacoustic response of the bell tower structure. In particular, the simulation environment requires the use of an uncompressed acoustic signal in *.wav format. The input audio file was recorded using a Class I USB omnidirectional microphone (UMIK-1, miniDSPTM, Hong Kong, China), which provides a flat frequency response and uniform sensitivity across directions. This type of microphone ensures minimal distortion and is well suited for accurately capturing the spectral content of the bell sound, which is the key quantity of interest for the simulation.  
The aim of the acoustic acquisition was not to reconstruct the full spatial distribution of the sound field, but rather to obtain a representative broadband excitation signal in the time-domain, suitable for use in vibroacoustic modeling. The procedure followed methodologies adopted in previous vibroacoustic studies [20; 21], including those related to musical instruments and heritage sound sources, where the primary goal is to reproduce the energy input rather than spatial variations.  
The recording was performed at 2 m from the bells, during a sunny day with stable weather conditions, to avoid the influence of wind or other environmental disturbances. No anthropic activity was detected during the recording period, ensuring a low back  
Figure 2: Photo of two of the northern (indicate the orientation) bell tower facade, where two of the existing church bells are visible.  
ground noise level. A windshield was also used to protect the microphone from local airflow variations.  
The microphone was calibrated using the class-I calibrator ND9B, producing a tone with a peak of 1000 \(\pm\) 0.01% Hz and two alternative sound pressure level settings, at 94 dB and 114 dB. Data were recorded and digitized as uncompressed *.wav files, with a sampling rate of 44,100 Hz. The recorded bell sound lasted for three minutes; a sub-set of the time-domain sound source signal, lasting 12 s and used as input for the structural vibration analysis.  
The recorded audio file was analyzed in the frequency-domain in MATLAB 2022 environment to derive the bell signal frequency peaks. In particular, the following peaks, measured in units of Hz, were detected: 127.3 Hz; 229.3 Hz; 280.5 Hz; 289.3 Hz; 330.7 Hz; 408.4 Hz; 560.3 Hz; 792.0 Hz; 856.3 Hz; 953.7 Hz; 1184.0 Hz; 1485.0 Hz; 1550.0 Hz; 1928.0 Hz; 1986.0 Hz; 2587.0 Hz; 3221.0 Hz; 3874.0 Hz; 4552.0 Hz; 5888.0 Hz; 6558.0 Hz. No relevant peak was detected above 10,000 Hz.  
Following the spectral analysis of the recorded bell signal, a relative sound pressure level (SPL) spectrum was computed and is shown in Figure 3. The SPL(f) was obtained by applying a fast Fourier transform (FFT) to the 12 s acoustic waveform and calculating the amplitude spectrum, which was then expressed in decibels (dB) and normalized to the peak value. This graphical representation highlights the frequency components with the highest acoustic energy and provides a more intuitive understanding of the bell excitation signal, complementing the list of frequency peaks reported above.  
Additionally, a power spectral density (PSD) analysis was carried out to evaluate the energy distribution of the signal across frequencies. The resulting PSD spectrum, shown in Figure 4, was computed using the Welch method and confirms the presence of dominant peaks already observed in the SPL representation, while offering a smoothed view of the signal's spectral energy content.  
Figure 3: Normalized relative SPL spectrum of the bell signal (FFT-based, 12 s segment, 0–6000 Hz, in dB).