Helmholtz resonators (HR) to control tonal noise propagation inside a duct can be made adaptive with an adjustable volume to allow their resonance frequency to track changes in the frequency of the tone to be controlled. As the resonator is intended to minimise the downstream transmitted sound power, a measure of this quantity would be an ideal cost- function to tune a resonator. As it is desirable to have a completely self-contained resonator with no external transducers, it is necessary to be able to estimate the sound power transmission from measurements inside the resonator package. This book describes two cost-functions based on pressure measurements inside the resonator that are representative of the downstream transmitted sound power in the duct. In addition, the book describes numerical and experimental approaches that were used for deriving and verifying these cost functions. This book will not only interest academics and students associated with the field of acoustics but also noise control industry personnel who need to consider a safety factor when designing a HR for tonal noise attenuation in the ducts.