Chapter 26, Problem 39A

Why is it dangerous for people in the balcony of an auditorium to stamp their feet in a steady rhythm?

To determine

The effect of rhythmic stamping of people’s feet in the balcony of an auditorium is to be determined.

Answer to Problem 39A

It is dangerous because the rhythmic stamping of people’s feet in the balcony will result in the collapsing of the balcony.

Explanation of Solution

Introduction: The concept to understand why we are told not to walk in uniformity over a suspended system whether it is a foot over bridge or a balcony or a bridge. Basic reason behind this is the concept of resonance.

The reason behind this is that the frequency of rhythmic stamping of feet matches the natural frequency of the balcony resulting in the resonance to occur. This resonance causes an increase in the amplitude of vibration of the balcony and ultimately resulting in its collapsing.

Conclusion: Resonance between the feet of audience stamping in rhythm and natural frequency in the balcony leads to collapsing of the balcony.