Low-frequency ground impedance measurement using a folded duct and wave number transforms

Abstract

Measuring the impedance of the ground at frequencies below 200 Hz is a difficult job due to the large apparatus needed. The well-known method of measuring the standing wave ratio and nodal locations in the sound field inside a duct terminated with the impedance material becomes impractical. In order to scan the standing wave field, a large tube arrangement is needed. Therefore, a folded duct is fabricated that is over 8 m long but only 1.5 m high. A loudspeaker excites a standing wave in the duct, which has one end pressed into the soil approximately 10 cm, and an array of microphones measure the standing wave response. The Fourier transform for each microphone signal and the a spatial wave number transform (Bartlet beamforming) across the array to extract the reflection factor and impedance are then computed. The result is a nicely separated incident and reflected wave seen as two peaks in the wave number spectra. For very low frequencies (<50 Hz), a cardioid beam pattern is used to separate the incident and reflected waves. Simulation results showed accurate impedance measurements using this method down to below 20 Hz if microphones are spaced 0.1 m apart.