Modal Analysis (was Negative bearing (long))

[Richard Brekne]

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Phil, Ron, and Del.

Here is a page from the text of Wograms article that addresses directly I think
Phils remarks, and what I interpret as his assertion of the predictability of
modal analysis from the unloaded to the loaded conditions. I would highly
recommend this whole article to anyone interested or directly involved in work
relating to soundboard impedance issues. Even for someone like me who just wants
to gain better insights such reading is valuable... so read away folks..


http://www.speech.kth.se/music/5_lectures/wogram/index.html



     In experimental work with upright pianos, a complete assembly
     of the instrument is normally used. Such an assembly
     consists of the wooden frame, soundboard, and metal plate,
     including the strings tuned to nominal pitch. This means
     that the soundboard is under the same load as in the finished
     piano. However, great care must be taken to ensure that the
     strings are muted so they cannot vibrate during the measurements.
     For this purpose, narrow strips of felt are woven through
     the strings as mentioned above. This operation wastes valuable time,
     and the question therefore arose as to whether the
     experiments could be conducted on a soundboard without strings, or at
     least with the tension brought down, without seriously
     changing the results.

     To answer this question, measurements were conducted on
     a completely strung assembly of an upright piano for which
     the  pitches were successively lowered (A4 = 440, 415, 220,
     and 0 Hz). Finally, the strings were removed altogether. By
     these  changes, the load on the soundboard was progressively
     reduced to zero, which would change the bending stiffness of
     the soundboard. When the strings were removed, the
     vibrating mass was also changed. Plate theory tells us that
     both the magnitude of the impedance, as well as the resonance
     frequencies will change when these parameters are changed.

     The experiments showed that detuning the strings by a
     semitone, or even an octave, produces only a small change in
     bending stiffness. This can be seen in the impedance curves for
     the first three conditions, which are practically identical
     (see Fig. 7). Not until the tension was completely let down could an
     influence on the impedance curve be observed (Fig. 7 d). In
     the lower frequency region, the soundboard resonances were
     shifted downward. The lowest resonance (leftmost valley on
     the Z-curve) was shifted from 115 to 90 Hz when the string tension
     was let down completely, while the resonances above 200 Hz remained
     essentially uninfluenced.



          Fig. 7. Influence of string tension on the input
     impedance (MP 7):
          (a) Normal tuning (A4 = 440 Hz),
          (b) a semitone lower (A4 = 415 Hz),
          (c) an octave lower (A4 = 220 Hz),
          (d) slack strings, and
          (e) strings removed.


     When the strings were completely removed, the lowest
     resonance was shifted further downward (to 70 Hz), and now
     the upper resonances were also lowered (Fig. 7 e). However,
     the general configuration of the impedance curve remained
     practically unchanged.

     The sound radiation curves show a somewhat different
     picture. Above approximately 1000 Hz the sound radiation
     does not change to any appreciable degree - the changes are
     evident only in the middle and lower frequency regions.
     Again, the general configuration of the curve remains practically
     unchanged.

     Summing up, stringing the back and tuning the strings
     to playing pitch are not absolutely necessary for obtaining
     representative measurements of the properties of a soundboard. The
     basic characteristics of the impedance and sound radiation
     curves remain essentially unaffected when the string load is
     removed. Only the lower resonances are influenced, resulting
     in an upward shift of about 50 Hz when the strings are pulled
     up to pitch. This can, however, easily be taken into account
     when analyzing the data.




--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:rbrekne@broadpark.no


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