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# TheoSol_I - IPhO2002 THEORETICAL COMPETITION Tuesday July...

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IPhO2002 I- 1 THEORETICAL COMPETITION Tuesday, July 23 rd , 2002 Solution I: Ground-Penetrating Radar 1. Speed of radar signal in the material v m : constant z -constant t tz w b bw - = =+ (0.2 pts) b w = m v 2 / 1 2 / 1 2 2 2 1 ) 1 ( 2 1 + + = w e s me w m v (0.4 pts) 1 ) 1 1 ( 2 1 2 / 1 = + = m v (0.4 pts)

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IPhO2002 I- 2 2. The maximum depth of detection (skin depth, d ) of an object in the ground is inversely proportional to the attenuation constant: (0.5 pts) (0.3 pts) (0.2 pts) 1/ 2 2 1/2 2 2 2 22 1 1 11 1 1 . 2 a d m es m m w w w ew = ===     +-  +-      2 / 1 2 = m e s d . Numerically ( 29 s e d r 31 . 5 = m, where s is in mS/m. (0.5 pts) For a medium with conductivity of 1.0 mS/m and relative permittivity of 9, the skin depth ( 29 5.3 19 15.93 m 1.0 d == (0.3 pts) + (0.2 pts)
IPhO2002 I- 3 3. Lateral resolution: Antenna (1.0 pts) r =0.5 m, d =4 m: 1 2 2 14 2 2 16 ll  =+   , 2 3 2 40 + -= (0.5 pts) The wavelength is λ =0.125 m. (0.3 pts) + (0.2 pts) The propagation speed of the signal in medium is r r o o r o r o m v e m e m e e m m me 1 1 1 1 =

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TheoSol_I - IPhO2002 THEORETICAL COMPETITION Tuesday July...

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