This article describes the theory and a simple experiment carried out to demonstrate the phenomenon of Anderson localization in an acoustical context. This is an effect whereby the propagation of vibration in a structure which is not entirely regular is impeded by the irregularities, giving rise on the average to an exponential decay of vibration level away from the driving point, even in the absence of any dissipation. The structure used in the experiment was a stretched string with masses attached to it. This string was studied with regular spacings of the masses and after the masses had been moved in a controlled way to provide a small degree of irregularity. In both cases, the transmission of energy from end to end of the string was measured as a function of frequency, and also the mode shapes in the second and fourth passbands were measured so as to demonstrate the underlying physics of the localization phenomenon, in which the individual modes making up each passband change from being extended throughout the structure in the regular case to being localized in specific areas of the structure in the presence of irregularity. All measurements yielded satisfactory agreement with the theoretical predictions.