  A procedure for measuring material thickness by means of necessarily-long
acoustic wavelengths is examined. The approach utilizes a temporal phase lag
caused by the impulse time of wave momentum transferred through a thin layer
that is much denser than its surrounding medium. In air, it is predicted that
solid or liquid layers below approximately 1/2000 of the acoustic wavelength
will exhibit a phase shift with an arctangent functional dependence on
thickness and layer density. The effect is verified for thin films on the scale
of 10 microns using audible frequency sound (7 kHz). Soap films as thin as 100
nm are then measured using 40 kHz air ultrasound. The method's potential for
imaging applications is demonstrated by combining the approach with near-field
holography, resulting in reconstructions with sub-wavelength resolution in both
the depth and lateral directions. Potential implications at very high and very
low acoustic frequencies are discussed.
