Chapter 15, Problem 51A

To determine

To Explain:The reason for which the soldiers walk out-of-step with each other as they cross the bridge.

Explanation of Solution

Introduction:

When the natural frequency of a body matches with the frequency of the applied periodic force, then the body starts to vibrate rapidly with an amplified amplitude. This phenomenon is termed as resonance.

When the marching soldiers cross the bridge, they walk out-of-step with each other. If soldiers march in steps, the periodic forces applied by them are in phase and thus, forced vibrations of a particular frequency are generated in the bridge. In case the natural frequency of the bridge is the same as the frequency of the soldier’s steps, the bridge will vibrate with increased amplitude due to resonance that may result in breaking of the bridge.

Conclusion:

The soldiers walk out-of-step with each other because if the frequency of their steps matches, the bridge’s natural frequency, resonance will occur that may result in breaking of the bridge.