3D40.10 - Xylophone
Demonstrate the vibration of solid bars, or how a transverse wave is propagated through a dense material.
InstructionsAn array of thin metal bars is mounted on two nearly parallel rods. Each bar is supported at two points near the ends, which are roughly equivalent to the nodal points. When struck with a mallet the bar experiences a transverse vibration.
The bars vibrate due to restoring forces in the metal. When a bar is struck with the mallet, a transverse wave is propagated through the bar. The velocity of the propagation is described by the expression v = sqrt(y/rho) where v = velocity of propagation, y = young's modulus of the rod material, rho = density of the bar material.
The wavelength of these bars vibrating in the fundamental mode is given by lambda = 2L where L is the length of the bar. The fundamental frequency f is given by f = (1/2L)*sqrt(y/rho).
A tuning fork , which is merely a bent bar, can be discussed as a straight bar where one end is fixed and the other free, causing the nodes to be close together where the bar is vibrating.
Extension: It is often thought that the nodes of a bar clamped at two points would be one quarter the distance from each end. This is not true. The nodes are at a distance of 0.224*Length from the ends.