# Why does the wave equation support wave motion?

by DunWorry
Tags: equation, motion, support, wave
 P: 40 If motion of an object obeys the wave equation, then it will display wave like behaviour. If you solve the wave equation, you get things like y = Asin $\frac{2∏}{\lambda}$(x - vt) which is a sinosodial wave. But from the second order differential equation v$^{2}$$\frac{d^{2}y}{dx^{2}}$ = $\frac{d^{2}}{dt^{2}}$ how can you tell intuitively that it describes something like a wave? Thanks
 Quote by DunWorry But from the second order differential equation v$^{2}$$\frac{d^{2}y}{dx^{2}}$ = $\frac{d^{2}}{dt^{2}}$ how can you tell intuitively that it describes something like a wave?