## 4 Leak Detection Technologies
### Hardware-Based Methods
#### 4.1.2 Acoustic Methods  
Acoustic methods represent a significant subset of hardware-based techniques for water leak detection, relying on sound and pressure variations to identify leaks. Since the 1850s, the utilization of listening sticks, or stethoscopes, has served as a conventional technique for leak detection [44]. These mechanical instruments, fabricated from metal, wood, or plastic, are deployed to audibly discern leaks on fittings, hydrants, or service connections and precisely determine their location. When water forcefully escapes from a high-pressure leak, it generates vibrations that propagate through the pipeline as structure-borne noise. This auditory signal is subsequently conveyed through the steel shaft of the listening stick, audible through an earpiece [28]. Primarily implemented on metallic pipelines featuring diameters ranging from 75 mm to 250 mm and operational under pressures exceeding 10 m [30], listening sticks underwent development in the mid-1960s. This evolution facilitated the integration of battery-powered sound amplifiers into these devices, consequently enhancing their leak detection capabilities [44]. These amplified devices, known as ground microphones or geophones, function analogously to their mechanical counterparts. Geophones identify subterranean noise from surface-level positions, which is particularly valuable in areas characterized by minimal fittings. Distinguishingly, geophones exhibit the capacity to detect leaks in plastic pipelines, low-pressure environments, and regions beset by elevated noise interference originating from factors such as traffic, water utilization, ground perturbations, and wind [45]. Nonetheless, this method is time-intensive, and its effectiveness is contingent on the operator's experience [46]. The leak noise correlation method relies on comparing the noises detected at two different measurement points within buried pipelines. Assuming consistent pipe material and diameter, noise travels at a constant velocity from both directions of the leak. The sensors detect the leak signals, which are wirelessly transmitted to a correlator that uses the cross-correlation method to pinpoint the leak location. Ideally, if the leak is equidistant from the two sensors, the noise would be detected at the same time. However, in most cases, the leak is located asymmetrically between the measurement points, resulting in a time shift measured by the correlation process [46]. Figure 7 demonstrates the fundamental principle of this method. The time delay between the two signals is determined by the location of the sensors at easily accessible points, such as valves or fire hydrants, and can be calculated as follows:  
\[\Delta\mathrm{T}=\mathrm{T}_{2}-\mathrm{T}_{1}=\frac{\mathrm{L}_{2}-\mathrm{L}_{ 1}}{\mathrm{V}} \tag{1}\]  
Here, \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\) denote the arrival times of signals 1 and 2, respectively, \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) represent the distances from the leak to sensors 1 and 2, and \(\mathrm{V}\) is the sound propagation velocity in the pipe. The distance from the closer sensor to the leak site can be calculated by substituting \(\mathrm{L}_{2}=\mathrm{D}-\mathrm{L}_{1}\) in Equation (1), where \(\mathrm{D}\) is the distance between the two sensors:  
\[\mathrm{L}_{1}=\frac{\mathrm{D}-\mathrm{V}\Delta\mathrm{T}}{2} \tag{2}\]  
Leak noise correlation requires a noise signal that can be generated using accelerometers and hydrophones. Accelerometers sense the acceleration of vibration induced by leak signals and can be installed directly on the pipe or attached to fire hydrants or underground valves. These sensors are more responsive at high frequencies and work well for metallic pipes [46]. On the other hand, hydrophones sense the sound induced by leak noise in the water core of the pipe and are placed at fire hydrants or air-release valves using special fittings. These devices are more effective than accelerometers for low-frequency leak signals encountered in the case of plastic pipes and larger-diameter mains [30].