Results of the analysis of acoustic-emission signals generated due to ultrasonic waves propagating in a polymer composite material and registered with piezoelectric and fiber-optic sensors are presented. The fiber-optic sensors were arranged into an adaptive interferometer based on using a dynamic hologram formed in a photorefractive crystal. Reducing the setpoint fading has made it possible to improve the noise immunity and sensitivity of the measurement system when using an adaptive interferometer on a photorefractive crystal. Optical fibers in the interferometer’s measurement system served as sensors of ultrasonic waves and were built into a polymer composite material when the sample was manufactured. The sample was a rectangular plate made of a multilayer fiberglass material. It has been discovered that the sensitivity of the adaptive interferometer makes it possible to detect acoustic- emission signals generated by a Hsu–Nielsen source. When determining the speed of sound in the polymer composite material, peculiarities of registering a group wave by fiber-optic sensors have been established that are due to the anisotropy of the medium the wave propagates in and the distributed character of sensor placement in the studied composite material. The wavelet transform has been used to separate the informative component of the wanted signal.