Using a reverberant chamber, it is possible to radiate a partially coherent ultrasonic beam into a free field. This type of acoustic secondary source is shown to be analogous to the Lambertian source in optics. The features and potential uses of this type of field are in marked contrast to the case of fully coherent ultrasonic radiation produced by plane or focussed transducers. The partially coherent secondary sources are not difficult to construct in a laboratory setting, and provide a useful alternative in ultrasonic measurements of materials properties, and other applications such as imaging.