The patterns generated by the kaleidophone (above) were described in more detail by the mathematician and physicist Jules Lissajous, later in the nineteenth century. He studied the curves created by the combination of two perpendicular vibrations. In order to visualize these curves he designed an instrument consisting of two little mirrors mounted on tuning forks. If the tuning forks sound in a ‘pure’ interval, the resulting image is static and symmetric. If the interval is not ‘pure’, the result is a chaos of lines. Smaller interferences between the two frequencies translate into subtle movements of the generated patterns. (https://en.wikipedia.org/wiki/Lissajous_curve)
Cathode Ray Tube (CRT): If we allow one AC signal to deflect the beam up and down (connect that AC voltage source to the "vertical" deflection plates) and another AC signal to deflect the beam left and right (using the other pair of deflection plates), patterns will be produced on the screen of the CRT indicative of the ratio of these two AC frequencies. These Lissajous figures are a common means of comparative frequency measurement in electronics. (http://www.vias.org/feee/acmeter_03.html)
