# Mechanical Resonance: Can Soldiers' March Cause 16 Hz?

• opuktun
In summary, a bridge with a natural frequency of 16 Hz will experience mechanical resonance if a battalion of soldiers marches across it.
opuktun
Q: If a bridge has a natural frequency of 16 Hz and assuming that a battalion of soldiers marches across it, will mechanical resonance occur?

Personally, I was quite unclear about the physical implication of "16 Hz". In my interpretation, I feel that to cause a mechanical resonance on the bridge, at a particular spot of that bridge, 16 cycles of march per second is required. But to make a spot to experience these 16 cycles per second is not very possible. Henceforth, I would like to check with the experts out there to see if I have made some errors in understanding.

I would really appreciate some feedback. Thanks! :)

You are forgetting about harmonics: excitations at 2, 4, and 8 Hz will also excite a 16 Hz resonance.

Actually, 16 Hz is the fundamental frequency. Sorry, I did not clarify properly.

Bridge designers commonly check for 2 Hz resonances as that is about what you can expect from foot traffic, even in cadence. I think Henry Petroski has a good section on that in one of his books, though I can't remember which. American Scientist also ran a piece on this within the past twenty years though that might well have just been Petroski again.

By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.

TVP45 said:
Bridge designers commonly check for 2 Hz resonances as that is about what you can expect from foot traffic, even in cadence. I think Henry Petroski has a good section on that in one of his books, though I can't remember which. American Scientist also ran a piece on this within the past twenty years though that might well have just been Petroski again.

TVP45 said:
By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.

Hi TVP45, thanks for the reply. Well, it's a theoretical question given in my tutorial. But I have not been touching my physics materials for five years? heh :P

And, BTW, designers do screw up. Here in Pittsburgh, a major new bridge span (less than 20 years old) fell off its rocker Thursday. Ouch!

## 1. What is mechanical resonance?

Mechanical resonance is the phenomenon that occurs when an external force is applied to a mechanical system at its natural frequency, causing the system to vibrate with a larger amplitude.

## 2. Can soldiers' march cause 16 Hz?

It is possible for a group of soldiers marching in unison to create vibrations at a frequency of 16 Hz, which is within the range of human hearing. However, the intensity of these vibrations would depend on factors such as the size of the group, the surface they are marching on, and the distance from the observer.

## 3. How does mechanical resonance affect soldiers?

If soldiers are marching in a formation that is in sync with their natural frequency, mechanical resonance can amplify the vibrations and cause discomfort or even injury. This is why soldiers are trained to march in different formations and to vary their pace to avoid resonance.

## 4. Can the 16 Hz frequency from soldiers' march cause structural damage?

The 16 Hz frequency produced by soldiers' march is unlikely to cause structural damage to buildings or other structures. However, if the soldiers are marching on a bridge or other delicate structure, there is a possibility that the vibrations could cause damage if they are in resonance with the natural frequency of the structure.

## 5. How can mechanical resonance be prevented in soldiers' marches?

Mechanical resonance in soldiers' marches can be prevented by varying the formation and pace of the march, as well as ensuring that the soldiers do not march in perfect unison. Additionally, using dampening devices or materials can also help reduce the impact of vibrations on soldiers and structures.

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