Problem 1 [20 points]: 3D wave speeds have been calculated using ultrasonic transducers. The estimated values are vL = 6200 m/sec, vS = 3200 m/sec. Assuming the material density as p=2700 kg/m3, compute: a) Young Modulus E [N/m2], Poisson ratio v, and Shear modulus G [N/m2]. b) Compute the Acoustic Impedance Z [with appropriate units] of the material. Problem 2 [30 points]: A wave is propagating in an aluminum block surrounded by water (you can consider Material 1 as Aluminum and Material 2 as Water). The pressure amplitude of the incident wave is 10 N/m2. (Aluminum) (Water) Density=2,700kg/m' Density=1,000kg{m Speed = 6,200m/sec Speed = 1,500misec a) Compute Pr, Pt of the reflected and transmitted waves and show a drawing of the waves similar to the one in the notes. b) Show that there is conservation of energy. Problem 3 [30 points]: A Longitudinal wave was generated in Material 1 (glass) and impinges with an angle OL,I=20deg on the interface with a second Material 2 (Aluminum). Speeds are: Glass V=4 km/sec; Vs=2.4 km/sec, Aluminum vL=6.3 km/sec; v8=3.3 km/sec a) Compute angles of propagation for all the reflected, refracted and mode converted waves Complete the drawing provided below with all waves involved. b) Compute the first and second critical angles. Motz mnd 1 Mdeaimd 2 Problem 4 [20 points]: A 20in thick concrete slab is inspected using the impact echo method. The Fast Fourier Transform (FFT) obtained at a test location is given here: Relative Amplitude Frequency (kHz) The speed of the longitudinal wave in the region of concrete tested is 10,000 feet/sec. Please assess the condition of the deck at such location by leveraging calculations and provide a clear explanation