This wave machine was made by the company Elliott Brothers in the late-19th century, after a design by Baden Powell (1796-1860). Powell was Savilian Professor of Geometry at Oxford from 1827 and was also the father of Robert Baden-Powell, founder of the boy scout movement. In his 1841 book Powell wrote:
"For the sake of those readers ... who may be commencing their acquaintance with the undulatory theory, it may not be out of place here to mention a method of imitating the different kinds of vibrations producing a wave by mechanical means. ... A glance at an illustration of this kind enables the mind to grasp the idea at once, even when unaccustomed to the mathematical analysis of it. (1)
Much of Powell's early work was on the wave theory of light, but in later years he moved away from physics as the mathematics became more and more complex.(2)
Powell's wave machine was based on one constructed by George Biddell Airy (1801-1892) some years before. Unfortunately, no details of Airy's machine appear to have survived.