Adjust your meter for the velocity of sound through copper, table of materials below, copper 4700 m/s. Unfortunately if you are sizing flaws, you are going to need a calibration block of copper with known indications of a certain size, becasue as you mention the impendence ratio is different for copper (different size/structure grains), and the same flaw in these materials won't show exactly the same response on the meter.
Material Metres/second
Air 330
Aluminium 6300
Alumina Oxide 9900
Beryllium 12900
Boron Carbide 11000
Brass 4300
Cadmium 2800
Copper 4700
Glass(crown) 5300
Glycerine 1900
Gold 3200
Ice 4000
Inconel 5700
Iron 5900
Iron (cast) 4600
Lead 2200
Magnesium 5800
Mercury 1400
Molybdenum 6300
Monel 5400
Neoprene 1600
Nickel 5600
Nylon, 6.6 2600
Oil (SAE 30) 1700
Platinum 3300
Plexiglas 1700
Polyethylene 1900
Polystyrene 2400
Polyurethane 1900
Quartz 5800
Rubber, Butyl 1800
Silver 3600
Steel, Mild 5920
Steel, Stainless 5800
Teflon 1400
Tin 3300
Titanium 6100
Tungsten 5200
Uranium 3400
Water 1480
Zinc 4200