Resonance

[Matthew Robinson]

Hello!

 

Earlier this year in A-level physics, we covered the topic of resonance. If you played the right music with an animated enough audience, presumably you'd get resonance in a venue which could cause structural problems? Is there any way of working out the resonant frequency of a venue with a calculator, spreadsheet and knowledge of maths and physics?

 

Thanks,

Matthew

 

E2A: Preferably theoretical methods, rather than by experimenting!

[AndyJones]

A building that I do a lot of rigging in has a resonant frequency. If you play the right note all the metal work vibrates with the same note. It's quite an interesting sight/sound!

[Jivemaster]

Most venues will have certain resonances these are features of the dimensions of the room. If the room has parallel (cuboid) sides then initial resonances will be at the frequencies determined by the separation of the parallel faces and the speed of sound in air (which of course varies with temperature and humidity)! After the prime modes are accounted for there will be other modes to consider which may be of less significance according to the surface of the walls.

 

probably a google search for "eigentones" will help your search.

[Matthew Robinson]

Ah, excellent. Thanks, Jivemaster!

[the kid]

Is this not really in the realms of the brown note?

 

I don't know much about sound really but is there really any point in working it out? Has anything occurred that has been caused by sound?

Possibly watching the Mythbusters episode on the brown note is a start.

[Matthew Robinson]

Has anything occurred that has been caused by sound?

 

Probably not, but if you add a crowd who take it upon themselves to jump up and down in time to the music...

[kerry davies]

Now when I were a lad, back in Jericho.....

[Jivemaster]

Several of the easily available texts on acoustics will mention eigentones and fully explain their intricasies, BUT that can be high level maths.

 

In a cuboid room the prime eigentones are determined by the parallel walls' spacings then reflections across diagonals in the room, then reflections off more than two faces.

 

Various room functions need more or less resonance and evenly distributed resonances can usually be tamed as needed. gaps in eigentones can give certain venues a particular acoustic colour, which may or may not be good.

[paulears]

You've also got to take in resonances produced by spaces outside the main area, as essentially you will have a number of further tuned cavities - so rooms and voids can all have an impact. On top of this you've then got to consider all the other objects with a natural resonating frequency in the audio band, that can be excited by energy in the room. These things can be almost impossible to predict, and even if you could, the sheer quantity of calculations required would be enormous. You also have the structure of the building to consider - what it's made of and how it is supported and damped. Maths far, far above my level.

[Matthew Robinson]

So it's effectively a problem that can be solved but would take too long? I suppose the model would be massively complicated for anything much more complicated than a cardboard box...

 

Furthermore, it would seem that every different situation would require a totally new model and movement of ANYTHING would require the whole model to require recalculation.

 

So, a simple solution isn't going to be found, even if I am able to differentiate inverse hyperbolic trig functions...

[Stan Hope-Streeter]

Has anything occurred that has been caused by sound?

Probably not, but if you add a crowd who take it upon themselves to jump up and down in time to the music...

 

Feyenoord Staduim used to have that problem.

[Jivemaster]

The laws of diminishing returns also apply to the studying of eigentones. The most significant first few eigentones can be determined easily and may possibly need taming, the next -less significant ones cost more to find- and reward you less in performance tonality. as you procede the costs begin to outweigh the benefits.

 

Concert hall acoustics, and broadcast and recording studio acoustics are often different by design. Some rooms have deliberately localised properties such as dead and live ends. Some rooms have variable properties by such as moving panels or rotating slats, these need careful usage!

[Simon Lewis]

If you played the right music with an animated enough audience, presumably you'd get resonance in a venue which could cause structural problems?

 

Many posters have concentrated on acoustic standing waves - which can certainly cause problems in terms of critical listening, sound reinforcement and speech intelligibility. For structural damage to be a concern, you would normally be looking at quite high levels of vibration. Whereas it's possible for sound systems to cause vibration that may excite the building structure, this is (usually) small compared to such activities as dancing or co-ordinated crowd movement.

It can be difficult to calculate building resonance, as there can be different systems to consider, but if you were looking at building resonance during an earthquake, there are some general rules that can be seen here.

 

If you Google for room resonance and for building resonance, you will see information on the two different issues.

 

Simon

[Seano]

Has anything occurred that has been caused by sound?

Probably not, but if you add a crowd who take it upon themselves to jump up and down in time to the music...

 

I think I remember an example of that. Black Rebel Motorcycle Club in Leeds Town Hall, 2003. But then again, maybe it was a false alarm after all: clicky.

[kitlane]

The reference to an 'animated audience' implies the movement of specatators is to be considered. A full structural analysis could be done that would work out the resonances of the building structure but this would be a very specialised job for an engineer.

 

The following is an extract from BS 6399: Part 1 Loading for buildings. Code of practice for dead and imposed loads. Annexe A

 

"Examples of dynamic loading conditions for some specific structural types

A.1 Buildings and structures with areas subjected to dancing and jumping

Buildings and structures with areas subjected to dancing and jumping are liable to be subjected to

inadvertent or deliberate synchronized movement of occupants, sometimes accompanied by music with a

strong beat, such as occurs at pop concerts and aerobics events. These activities generate dynamic effects

that can result in enhanced vertical and horizontal loads on the structure. If, in addition, the synchronized

movement is at a frequency that matches a harmonic of the natural frequency of the structure, or a part of

it, resonance of the structure is liable to occur that greatly amplifies the dynamic response.

 

Two alternative approaches are recommended for such design situations:

a) Design to avoid resonance: In addition to design with dead and static imposed loads for buildings or

structures with areas subjected to physical activities and overcrowding, as given in rows C4 and C5 of

Table 1, resonance of the structure should be avoided. This is achieved by limiting structure’s natural

frequencies so that the vertical frequency is greater than 8.4 Hz and the horizontal frequency is greater

than 4.0 Hz. These frequencies should be evaluated for the appropriate mode of vibration of an empty

structure.

or

 

b) Design for dynamic loads: Buildings and structures with areas subjected to dancing and jumping

should be designed to resist the anticipated dynamic loading. The deformation of the structural frame

should not exceed limits appropriate to the building or structure type. Detailed design should be

undertaken to account for the dynamic response of the structure and a range of load frequencies and

types with the help of specialist advice and specialist guidance documents [1]."

 

The reference is to "BRE Digest 426, The response of structures to dynamic crowd loads. BRE, Watford, October 1997"

 

For temporary structure such as grandstands there is guidance in "Temporary Demountable Structures......" published by the Institution of Structural Engineers. This gives a notional horizontal load as a percentage of the vertical imposed load with three different values based on three categories of audience activity. i.e.

 

Sedate, Seated - Notional Horizontal load of 6% of vertical imposed load

Vigorous, lively, active - Notional Horizontal load of 7.5% of vertical imposed load

Synchronised - Notional Horizontal load of 10% of vertical imposed load

 

However, the latter only applies if the synchronised movement does not match the resonant frequency of the structure. If it does then a a full dynamic analysis is required.

 

A concurrent post has been automatically merged from this point on.

 

If you played the right music with an animated enough audience, presumably you'd get resonance in a venue which could cause structural problems?

 

Many posters have concentrated on acoustic standing waves - which can certainly cause problems in terms of critical listening, sound reinforcement and speech intelligibility. For structural damage to be a concern, you would normally be looking at quite high levels of vibration. Whereas it's possible for sound systems to cause vibration that may excite the building structure, this is (usually) small compared to such activities as dancing or co-ordinated crowd movement.

It can be difficult to calculate building resonance, as there can be different systems to consider, but if you were looking at building resonance during an earthquake, there are some general rules that can be seen here.

 

If you Google for room resonance and for building resonance, you will see information on the two different issues.

 

Simon

 

Are we ignoring that light bulb that was rattled loose at the St Alkmunds gig? :P