Question 2 (25 marks) a) An acoustic pressure wave propagating through a medium is described by: p =P, el where j = V=1 and is the phase of the wave. The so-called phase velocity of the wave is given by: d d o T dt 99 where fis time and x is the position along the direction of travel of the wave. (i) For anon-absorbing medium, the phase is described by = wt kx, where w is the angular frequency and k is the wavenumber. Show that: c= k (2] (ii) When the wave travels through an absorbing medium, the acoustic pressure decays exponentially such that: = p_ej{mtkrj_ecrx Where is the attenuation coefficient. Write down an expression for the phase under this condition, and show that the phase velocity is now equal to: (3] (iii) Show that c in an absorbing medium can also be expressed as: W : - ol \"VErar where 8 = tan~! (%) (5]