Mail
NEW

Schematic Newgrange for acoustic Helmholtz resonance

The dimensions of Newgrange can be seen from the below picture (O'Kelly [1982], a composition of page 88 and 108):

Making this a little bit more schematic (for doing Helmholtz simulation) one gets for the present day situation of Newgrange (no dimensions are mentioned here, see below table):

Each number in the picture refers in the below table towards a cylindrical segment with a length, an area and a volume

Segment	Start of segment seen from end seg7 [m]	End of segment seen from end seg7 [m]	Area start [m²]	Area end [m²]	Cumulative volume from end seg18 [m³]
Passage
1	13.78	10.2	1.4	1.4	-
2	10.2	5.8	1.5	1.5	99.0
2A	5.8	5.7	1.5	1.4	92.3
3	5.7	3.85	1.4	1.4	92.1
3A	3.85	3.75	1.4	1.5	89.5
4	3.75	3.16	1.5	1.5	89.4
4A	3.16	3.06	1.5	1.7	88.5
5	3.06	1.94	1.7	1.7	88.3
5A	1.94	1.84	1.7	2.0	86.4
6	1.84	0.58	2.0	2.0	86.2
6A	0.58	0.48	2.0	1.2	83.7
7	0.48	0	1.2	1.2	83.5
Chamber (possible start)
7A	0	-0.10	1.2	1.4	83.0
8	-0.10	-0.77	1.4	1.4	82.8
8A	-0.77	-0.87	1.4	1.8	81.9
9	-0.87	-1.42	1.8	1.8	81.7
9A	-1.42	-1.52	1.8	2.1	80.7
10	-1.52	-1.99	2.1	2.1	80.5
10A	-1.99	-2.09	2.1	2.4	79.5
11	-2.09	-3.66	2.4	2.4	79.3
11A	-3.66	-3.76	2.4	2.9	75.4
12	-3.76	-4.26	2.9	2.9	75.2
12A	-4.26	-4.36	2.9	3.2	73.7
13	-4.36	-5.36	3.2	3.2	73.4
14	-5.36	-7.81	21.3	21.3	70.2
15	-7.81	-8.26	8.3	8.3	18.0
16	-8.26	-8.97	6.4	6.4	14.3
17	-8.97	-9.63	7.4	7.4	9.7
18	-9.63	-10.56	5.2	5.2	4.8
Roofbox
31	11.38	11.12	0.78	0.78	-
31A	11.12	11.02	0.78	0.55	-
32	11.02	10.46	0.55	0.55	-
32A	10.46	10.36	0.55	0.27	-
33	10.36	10.2	0.27	0.27	-
Tunnel
Tunnel	11.1	-	-	-	49.2

Some remarks belonging to the above:

A segment dat ends with an A is a concical segment of 10 cm after the segment without the A
Segments without an A are cylindrical segments..
The roofbox (segments 31 to 33) is above segment 1; segment 33 ends at the same x-distance as the start of sgement 2.
Thestart and end of a segment is measured from the end of segment 7.
Some segments are flanged:

the start of segment 31 is flanged on all sides (floor [0 deg], sides [0 deg] and top [90 deg]).
the end of segment 33 is flanged on 3 sides (sides [0 deg] and top [0 deg] and floor not [180deg]).
the start of segment 1 is flanged on 3 sides (floor [0 deg] and sides [90 deg] and top not [180 deg]).
the end of segment 1 is flanged on 3 sides (floor [0 deg] and sides [0 deg] and top not [180 deg]).
the end of segment 7 is flanged on all sides (floor [0 deg], sides [90 deg] and top [60 deg])

There is a cumbrend stone (K1) in front of segment 1 (distance 168 cm and height stone 64 cm)
It is not precisely known where the tunnel starts, at this moment I have the idea it is at the end of segment 7.
The volume is given as a cumulative volume from segment 18 (end of chamber), this enables an easy change of chamber-volume if a different chamber/passage boundary is picked (when changing the chamber/passage boundary the cumulative length changes of course).
The tunnel has a volume of some 49.2 m³. It starts at the height of the start for segment 2 and it ends at the height of the end of segment 9.
The tunnel is connected to the passage by means of pipes between the orthostats with an area of around 5*5 cm and ~50 cm long; there are on average 2.8 pipes per meter.

Transmission line method

John Coltman used the above information to calculate the resonance frequency of the present day Newgrange setup (without including the holes and the tunnel). His results (using transmission line equations) are [Coltman, pers. comm. [2005]):

I used two estimates for the end correction on the passage -- 0.4 meters and 0.6 meters. With the roofbox entry assumed closed, I get the Helmholtz resonance frequencies as 1.87 and 1.85 Hz, respectively. Thus it is not very sensitive to the end correction assumption.
For the roofbox I estimated an end correction of .45 meters. The admittance of the roofbox, seen from the inside end, has a value of 11.5 relative to the characteristic admittance of the passage, at a frequency of 1.87 Hz. Segment 1 of the passage has an admittance of 7.3 or 7.0, depending on the assumption of .4 or .6 meter end correction. Thus the roofbox opening gets the major share of the acoustic current. Together, these two admittances add to 18.87 or 18.54. This is equivalent to a segment length of 1.55 or 1.58 meters. The Helmholtz resonance frequency with the roofbox open then becomes 2.08 Hz, with no significant difference whether we take .4 or .6 for the passage end correction.
A short program calculated the effect of the distributed holes to the tunnel, and found that they shortened the effective length of the passage by 2.5 meters in a segment with area 1.7 square meters. Running the program again with this shortened passage. I get a resonance at 2.4 Hz with the holes in place and the roofbox open.

Simulating an acoustic environment with an electrical one

Assuming that the acoustic circuit is in size much smaller compared to the acoustical wavelength (normally the case when looking into the low Helmholtz resonance, but not always; so check it always!), one can transform an acoustical environment into an electrical circuit, so that one can do an 'electrical' analysis in that environment (like using 5Spice).
The methods for determing R', C' and L' are described in this link.

I am thinking about the follow schematic for the present day Newgrange.

Ideas on acoustical circuits for Newgrange

Newgrange with holes in passage towards modern tunnel, but not many in chamber

So some ideas on the results of above model for the present day Newgrange:

a Helmholtz frequency of around 1.7 Hz when roofbox and entrance are both open. Holes in the passage (with a modern tunnel) and no holes in chamber.
There is another peak in the frequency response around 3.2 Hz (due to the Helmholtz resonance of the tunnel)
Both of these peak depend on the amount of holes between the chamber and the tunnel/passage.

If the above model maps nicely measurements done at Newgrange, it is very easy to transform the model to mimic the original state of Newgrange.

Disclaimer and Copyright

Home

Mail

Major content related changes: Jan. 12, 2006