Resonator sizes, and bar "side mounting" (Qs Mark Anderson)
-----Original Message----- From: Mark Anderson Sent: 17/05/06 2:03 AM To: email@example.com Subject: Low chimes?Hi Jim.
Thanks for the great information on your site.
I am working on a potential installation for a museum that started out as a "xylophone wall", but it's changing as the concept develops. I'm currently exploring resonators. I've tried working with 1/4 length resonators, but have had limited luck. Additionally, these bars will need to mount vertically with little room for a resonator to extend backward. I've got about a foot of depth to the wall they'll mount in.
I have had some luck with mounting my bar on the *side* of my resonator, but the math is completely perplexing to me. My prototype bar sounds an F4 and measures roughly 8 cm in width. however, by resonator is 16cm in diameter, with a length of about 110 cm. The hole over which my bar is mounted is about 1/3 of the way down the tube, and roughly matches the width of my bar. It's a nice sound, but that seems like a ridiculously large resonator for that note. Are the formulae different for side mounted resonators? Have I inadvertently made an open tube?
Any hints you could offer would be great. Thanks.
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Dear Mark - thanks for your email, and sorry its taken a week for me to get back to you...
At 260 hz a rough guess for 1/4 wavelength tube should be about 33cm so I reckon you might be in the wrong ballpark. Things do change a bit maths wise when trying to set it up the way you are with the hole on the side. 1/4 wavelength resonators actually act as helmholtz resonators, so you could look up the formula for volume : opening area if you like, but I don't know off hand. Using a cylinder with the opening at the end tends to work better, and makes the maths/measurement easier. Basic sound formula is wavelength equals frequency(hz) divided by velocity of sound in m/s (I forget exactly what it is now, but look it up - off the top of my head I think it might be about 360m/s. Once you've calculated your wavelength don't forget to divide by 4 (1/4 wavelength tube). The actual length should be a couple of cm shorter than this because of "end correction" - how much depends on the tube diameter - the formula is on the website somewhere ....
Why don't you try using a 90degree elbow as the open end of the tube. This will sit right under the middle of the bar, with the length of tube falling vertically behind the bar in much the same way that I imagine it currently is. The non-bar end of the tube should of course be closed.
The best diameter fir the resonator tube is typically very close to the width of the bar - for a bar 8cm in width you could use 80mm or 90mm pvc pipe quite easily. In Australia 90mm is much cheaper and more readily available as it is the standard for domestic stormwater.
I hope this is helpful to you - please don't hesitate to ask questions etc...
answers by Jim MCCarthy - 01/12/2005
For more help on instrument building you can email Jim.