A simple experiment can be performed to demonstrate the dispersive nature of flexural waves
Discussion of Time SignalsThe equation of motion for flexural (bending) waves in a beam is where is the speed of a quasi-longitudinal wave (Eis Young's modulus and ?Ѡis the mass density). This equation of motion is a fourth-order differential equation such that the solutions are not of the formy(x,t) = f(x-ct) + g(x+ct). In addition, the flexural wave speed is dispersive as evidenced by the fact that the wave speed is proportional to the square root of frequency. Thus, higher frequency flexural waves will travel faster than lower frequency flexural waves. A force pulse contains many (almost infinite) frequency components Hammer impact at Point 1
Hammer impact at Point 2(From Acoustics and Vibration Animations - Dan Russell, Kettering University) |