The compressional (P) and shear wave (S) velocities for Mg2SiO4 wadsleyite have been measured to 7 GPa and 873 K using simultaneous ultrasonic interferometry and in situ X-ray diffraction techniques. From the velocity measurements we obtained the pressure and temperature derivatives for the elastic shear (G) and adiabatic bulk (KS) moduli, (∂G/∂P)T=1.5(1), (∂G/∂T)P=-0.017(1) GPa/K, KS=173(2) GPa, (∂KS/∂P)T=4.2(1), and (∂KS/∂T)P=-0.012(1) GPa/K; for the P and S waves, we obtained (∂VS/∂P)T=0.021(1) (km/s)/GPa, (∂VS/∂T)P=-0.035(2) (km/s)/K, (∂VP/∂P)T=0.065(2) (km/s)/GPa, and (∂VP/∂T)P=-0.038(2) (km/s)/K (values in parentheses are standard deviations, e.g., 1.5(1)=1.5¿1). Independent equation of state analysis of P-V-T data provided an estimation of the temperature dependence for the isothermal bulk modulus of (∂KT/∂T)P=-0.022(12) GPa/K and thermal expansion (α=a+bT) coefficients of a=2¿10-5 K-1 and b=2.5¿10-8 K-2. Using these data along with elastic properties for other mantle phases, a velocity-depth profile for a pyrolite model to 670 km depth is constructed using a finite strain method along a 1673 K adiabat. In the transition zone the pyrolite model has a smaller gradient between 410 and 660 km than the body wave models from synthetic waveform analyses but converges with the seismic profiles at the bottom of the transition zone just above the 660-km discontinuity. The pyrolite model has velocity jumps of 6.9% and 7.9% for P and S waves, respectively, over a thickness of ~10 km for the phase transformation from olivine to wadsleyite, which is in good agreement with short-period P wave reflection data and a recent fine structure model (C4) for both the velocity jumps and the thickness of the 410-km seismic discontinuity. ¿ 2001 American Geophysical Union