We have constructed a high sensitivity apparatus using Faraday detection for studying the response of domain walls in localized areas (down to 100μ2) of bubble materials to sinusoidal or pulsed fields. Electronic techniques for studying pulse response with a resolution of a few nanoseconds and nonlinear response to sinusoidal excitation of constant amplitude out to 32MHz are described. Results of pulse response data on ( EuY ) 3 ( GaFe ) 5 O 12 films show underdamped oscillations when an in‐plane dc field is used to stabilize a stripe domain pattern. The frequency wc of the oscillations agrees with that expected from the classical “wall mass” and restoring force constant within 50%. The sinusoidal response vs frequency reveals two lower frequency resonances which increase rapidly towards wc as the in‐plane field parallel to the stripes is increased.