## Sounds of Music C

UTF-8 U+6211 U+662F
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### Re: Sounds of Music C

smayya337 wrote:
November 19th, 2020, 7:38 am
UTF-8 U+6211 U+662F wrote:
November 17th, 2020, 8:39 pm
smayya337 wrote:
November 17th, 2020, 5:39 pm
UTF reminded me earlier today that I hadn't written a question, so I'm back. Sorry! I can't think of many good questions, so I'll just use this one:

What is the ratio of the length of my Bb soprano clarinet (lowest note: concert D3) to that of my sister's Eb alto saxophone (lowest note: concert Db3)? (Assume the instruments abide by equal temperament with concert A4 = 440 Hz, that the speed of sound is 343 m/s, and that my sister somehow got her hands on a straight alto saxophone.) Provide three sig figs.
Really guessing but: 138.6 / 146.8 = 0.944?
Not quite... Here's what I did:
We know that $L=\frac{nv}{2F}$ for a conical woodwind (like a sax) and $L=\frac{nv}{4F}$ for a stopped cylinder (like a clarinet). Substituting the appropriate frequencies gives $L=0.584 m$ for the clarinet and $L=1.237 m$ for the sax. Dividing those two values gives a ratio of 0.472.
Hopefully my logic isn't too flawed, I'm still kind of rusty. Your turn!
Ahhh I assumed they were both the same shape oops

What is the equivalent length with end correction of the neck (2.2 cm long with an 11.8 mm diameter) of a 500 mL empty water bottle? Assume the neck and water bottle body are both cylindrical.

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