Energy in a String Wave

摘要

When one end of a taut horizontal elastic stringis shaken repeatedly up and down, a transversewave (assume sine waveform) will be producedand travel along it.1 College students know this type of wavemotion well. They know when the wave passes by, eachelement of the string will perform an oscillating up-downmotion, which in mechanics is termed simple harmonic.2They also know elements of the string at the highest andthe lowest positions—the crests and the troughs—aremomentarily at rest, while those at the centerline (zerodisplacement) have the greatest speed, as shown in Fig. 1.Irrespective of this, they are less familiar with the energyassociated with the wave. They may fail to answer a questionsuch as, "In a traveling string wave, which elements haverespectively the greatest kinetic energy (KE) and the great-est potential energy (PE)?" The answer to the former is notdifficu elements at zero position have the fastest speed andhence their KE, being proportional to the square of speed,is the greatest. To the PE, what immediately comes to theirmind may be the simple harmonic motion (SHM), in whichthe PE is the greatest and the KE is zero at the two turningpoints. It may thus lead them to think elements at crests ortroughs have the greatest PE. Unfortunately, this associationis wrong. Thinking that the crests or troughs have the great-est PE is a misconception.3