Klarinet Archive - Posting 000095.txt from 1996/05

From: Jonathan Cohler <cohler@-----.NET>
Subj: Re: A question about acoustics
Date: Mon, 6 May 1996 03:47:53 -0400

At 9:21 AM 5/6/96, Peter Bellen wrote:
>> Imagine a pulse (a very short, high pressure spike) traveling down the tube
>> to the open end. As the pulse "hits" the open end, the pressure must
>> always add to zero. Therefore, a negative pulse (a low pressure spike) is
>> reflected back (the negative pulse and the positive pulse sum to zero at
>> the node).
>>
>...
>>
>> State this mathematically and you get that the possible wave lengths are:
>>
>> 4L, 4L/3, 4L/5 etc.
>>
>> Or, in other words, the possible frequencies are:
>>
>> v/4L, 3v/4L, 5v/4L, etc. (only odd harmonics!)
>>
>> Do the same drawing excercise with a node at both ends and you will quickly
>> discover that the allowed wavelengths and frequencies are respectively:
>>
>> 2L, L, L/2, L/3, etc. (wavelengths)
>> v/2L, 2v/2L, 3v/2L, etc. (all harmonics)
>>
>> I hope this helps without getting too technical.
>>
>> ----------------------
>> Jonathan Cohler
>> cohler@-----.net
>>
>
>I fully agree with the above explanation (I admire the way you did it,
>without the wave equation and its boundary conditions), but I've still
>got one problem: how to explain the different behaviour of a soprano
>saxophone and a clarinet?
>
>Thanks,
>
>Peter Bellen
>peter.bellen@-----.be

A soprano sax has a conical bore. See my subsequent message about oboes
and bassoons (which also have conical bores).

------------------
Jonathan Cohler
cohler@-----.net