Re: wave propagation at liquid7solid interface : 2. You can find in many books concerning ultrasound formulas describing the reflections conditions.
: They work very good, but only, if your incidence angles are not narrow to the critical or 90 degrees.
: And I don´t know any good formula that can give you real good worth for the phase. We have made a program, that works in many cases.
: If you are interested in this problems - plese contact us.
A more general solution lies with matrix methods - the equations are more involved but will deal with the issues of critical incidence
angles and evenescent waves.
I have used solutions based on the work of Knopoff.
ref: L. Knopoff (1964) A matrix method for elastic wave problems. Bull. Seism. Soc. Am., Bol. 54, 431-438
The formulations allow the calculation of the compression and shear wave transmission and relfection coefficients for single or multiple interfaces for both compression
and shear wave incidence. These can be calculated as functions of incidence angle and frequency. Forexample, Fourier Analysis will give you the time domain impulse
response of the system.
The formulations are usually derived in the complex frequency domain and will yield the amplitude and phase of the transmission and reflection
coefficients. Depending on what formulation you use, they will give accurate results in situations where the incidence angle is high
leading to complex refraction angles. The formulations generally assume complex wave propagation which will allow you to calculate the effects
of loss in the system (eg frequency dependent attenuation and phase velocity)
A good review of these technqiues can be found in:
MATRIX TECHNIQUES FOR MODELING ULTRASONIC-WAVES IN MULTILAYERED MEDIA
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL, 1995, Vol.42, No.4, pp.525-542
Hope this info helps,
Dr. R.J. Freemantle
NDT Solutions Ltd
Keele University Science Park
Tel +44 (0)1782 584306
Fax +44 (0)1782 711093