When the crowd roars at Brann Stadium it can be heard from much of Bergen. A reader wonders whether the voices of soccer fans amplify one another. The answer takes us from the larynxes [and uvulas] of fans in Bergen to the old Aamodt Bridge over the river Akerselva in Oslo. (Photo: Enrique Cornejo, CC BY 3.0)

Are soccer roars self-amplifying?

Does the volume double when two persons yell together? A reader has questions about the hoots and hollers of the crowd at his local football stadium.

Vetle Skjold from Bergen writes: “Hi! I have a question I’ve been wondering about for years.

I live up on the hill above Brann Stadium. When there’s a football match on I can hear loud and clear the roar of the crowd when a goal is scored and the whistles of disapproval when the referee makes a mistake.

If just one person had stood alone down there on any other day and screamed there is no way I could hear it.

So my question is: ‘Why is it that when many yell together it is much more audible and deafens other sounds? Are multiple voices amplifying one another?’”

Cries do not amplify each other

“If he thinks there is some sort of mutual amplification of the voices he is wrong,” responds Sverre Holm, a professor in the University of Oslo’s Research Group for Digital Signal Processing and Image Analysis (DSB).

Holm has a special interest in acoustics and that is where the answer is found.

“When people yell together this is an example of incoherent addition,” says Holm.

And what is that? We start with the easiest part – addition.

Not oscillating together

When many people yell at the same time each voice adds to the total – so that is addition.

Just like one plus one is two, one soccer fan hollering plus another fan doing ditto gives twice the volume – the strength is double.

So… incoherent? Well, that might aptly describe some of the unintelligible chants of football fans, but this isn’t the meaning here. He means the voices of the fans are not coherent – the sound waves are not oscillating identically together.

No two vocal cords the same

Holm explains that even though thousands are yelling “Heia Brann” [C’mon Brann], each of their hollers is only linguistically alike. If you see the sound waves in each cry, all are somewhat different.

No two persons have identical vocal cords. And the Bergen dialect also includes abundant use of uvulas in “R” sounds, so we can include those little organs as contributors to the cacophony. Two human voices vibrate in slightly different ways. Sound consists of pressure waves that spread through the air, like the rings of waves on a pond.

When two voices yell out “Heia Brann” it is like two slightly different rocks were tossed into the pond simultaneously.

Add or subtract to each other

Two rings of waves spread out. The waves have various heights – amplitudes – and the distances between the crests makes for frequencies.

So the crests of two interfering waves meet at points – they get twice as high. In other spots the crest can meet the bottom of a trough of one of the rings of a wave. They cancel out one another – at these points we
have wave interference that flattens the waves out.

The average of the additions and cancelling out becomes just about a doubling of sound intensity if we have two sources of sound.

Noise cancelling headphones

“This last effect [peak meets trough] is the same as what is used in headphones that have active noise reduction,” says Holm.

These headphones have a microphone that picks up the sounds coming from outside – for instance traffic noise. They then turn all this sound upside-down so crests meet troughs.

This confrontation of opposite wave patterns, ones that are 180 degrees out of phase as acousticians say, creates a counter-noise that is sent back into headphones along with, perhaps, the music a person is listening to.

As crests and troughs from the disturbing noise and the counter-noise generated in the headphones meet, they flatten out, more or less, creating silence. Hypothetically, a user will only hear the sounds he or she wants to hear, like music off their smart phone. Such active noise cancellation works best for deep bass sounds, however. 

Would need a microphone by the eardrum

The higher-pitched sounds have shorter frequencies. Some outdoor noise has such short wavelengths that the microphone on a headphone cannot pick up and phase out all the sound reaching the user’s eardrum. So the noise reduction using even the costliest headphones is imperfect. 

“In order to get perfect noise cancellation for higher frequencies the microphone would have to be the same place as your eardrum, inside your ear,” says Holm.

Marching in step – coherent sound waves

So far we have described incoherent addition of sound. What about coherent addition?

This means that the soundwaves oscillate together. The effect is like many soldiers marching in step.

An inscription on an old suspension footbridge in Oslo, Aamodt Bridge, translates as follows: “100 men I can bear, but I fail if they march in step.”

In other words: A hundred persons can cross the bridge if their steps are your normal random mix of incoherent additions. However, if they all march together, stepping at the same time, the result is a coherent addition which the constructors thought might be enough to make the bridge fail.  Soldiers could start waves which could be something like that made by the winds at the Tacoma Narrows Bridge, which collapsed dramatically in 1940.

What does this have to do with those noisy football fans at the Brann Stadium? If they all managed the impossible feat of vibrating their vocal cords and uvulas the same – creating identical sound waves – the effect would be absolutely ear-splitting.

“The sound of ten football fans would not be ten times as strong as it is in incoherent addition. It would be 100 times as strong,” says Holm.


Read the Norwegian version of this article at forskning.no

Translated by: Glenn Ostling

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