  The behaviour of semi-dilute wormlike micelle solutions under vertical
vibrations is investigated using classical measurements of the Faraday
instability threshold along with two new experiments based on particle imaging
velocimetry and birefringence. We provide evidence for the presence of
oscillations of the critical acceleration and wave number with the vibration
frequency, which are linked to oscillations of the velocity and birefringence
fields along the vertical direction. These observations are interpreted in
terms of standing elastic waves across the fluid layer. Such an interpretation
is confirmed numerically by using the model proposed by S. Kumar [Phys. Rev. E
65, 026305 (2002)] for a viscoelastic fluid to calculate the velocity and
deformation fields. Finally, further birefringence experiments above the
instability threshold show that the Faraday instability does not induce
disentanglement and breakage of the micellar network.
