Consider the vibration of a circular membrane If we examine

Consider the vibration of a circular membrane. If we examine the nodal circles (circular symmetric lines of zero displacement) we find they are nearly equally spaced. Explain why this is?

Solution

The vibrations are caused by stationary waves. the waves travel from the center and get reflected back at the circumference traveling in opposite direction. For a stationary wave, nodes are point of zero dispalcement and anti-nodes are points of maximum dispalcement. The seperation between toe succesive nodes or anti-nodes is equal to half-wave length and is the charecteristic of the wave. Hence the nodal cicles are equally spaced.