Klarinet Archive - Posting 000196.txt from 2010/08

From: Diego Casadei <casadei.diego@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Tue, 17 Aug 2010 04:52:59 -0400

Diego Casadei wrote:
> Apologies. I should have read all other emails before replying.
>
> The main point is that the sound velocity may change. This happens with
> the pressure, but negligibly: the velocity is proportional to the square
> root of the _static_ variation on the pressure, which is negligible
> because the clarinet is an open tube and we don't create a powerful wind
> through it.

Better explanation from
http://www.sengpielaudio.com/calculator-speedsound.htm :

The static air pressure p and the density rho of air are proportional at
the same temperature. That means, the ratio p / rho is always constant
on a high mountain, and even at "sea level". Forget the air pressure,
but look accurately at the very important temperature.

In conclusion, the sound velocity in air is not dependent from the pressure.

> I think that the most important factor is refraction: at the exit and
> inside the bell the wavelength may change because of this, and the sound
> velocity has to reflect this. However, we should try to quantify the
> effect. To recover from the 8 cm displacement we need some change as big
> as 14%. Is this a realistic amount? If somebody has numbers I would be
> interested to know them.
>
> Cheers,
> Diego
>
>
>
> Diego Casadei wrote:
>> Tony Pay wrote:
>>>
>>> The fact remains, if I understand things correctly now, that having
>>> cylindricality is the only way that Diego's calculation method works.
>>
>> No. What I did is to use the well known relation
>>
>> wavelength * frequency = sound velocity
>>
>> and the known dependency of the sound velocity on the air temperature. I
>> did not account for the effective horn extension out of the bell, and my
>> computation does not make any assumption on the shape of the pipe.
>>
>> Unless the sound velocity is different inside the clarinet pipe, which I
>> found no indication for in my readings, the formula above gives the
>> correct wavelength.
>>
>> My frequency measurement can be off by 1-2 Hz (I have a cheap tuner),
>> which is at most a 0.4% change in the wavelength. A whole degree Celsius
>> uncertainty on the air temperature (which is incredibly exaggerated in
>> my case) would give a maximum change of 0.3% in the wavelength.
>> Together, they would give a maximum tolerance of 3 mm to my measurement,
>> which is much smaller than the distance to the vibrating reed.
>>
>> Cheers,
>> Diego
>>
>

--

Diego Casadei
__________________________________________________________
Physics Department, CERN
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