where ρ is the material density and v is the speed of sound. When an acoustic wave encounters an interface, the velocity, acoustic pressure and phase of the wave must be continuous across the interface. These conditions allow the calculation of the ratio of reflected and transmitted acoustic pressure as a wave moves from a material of impedance Z1 to a material of impedance Z2 at normal incidence: r = Pr / Pi = (Z2 -Z1) / (Z2 + Z1 ) t = Pt / Pi = 2Z2 / (Z2 + Z1) where Pr, Pt, and Pi are the reflected, transmitted, and incident acoustic pressures. Careful analysis of ultrasonic signals, along with prior knowledge of the system being measured, enable an experimenter to calculate these transmission and reflection coefficients and from them deduce a sample's acoustic impedance, density, and velocity. Note also that these relations only hold for normal incidence. Calculation of t and r from pitch-catch measurements requires more advanced analysis which is covered in more detail in .