Monochord experiment

[Michael Wathen]

Bob Hohf wrote:

>The traces seem to record voltage in the plates.  How does this voltage change
>relate to the string motion?  Does the voltage reflect the amplitude of the
>string, or (which seems more likely) the velocity of the wire as it
>oscillates?  This may seem like hair splitting, but, if it is velocity that
>changes the plate voltage, then the peaks of the tracing would occur as the
>wire is passing the centerline, or the rest point, of the travel.  Is it
>possible to infer the amplitude from the velocity?
>
>Your string was 78 cm long or roughly 10x the length of the plates.
>Considering the complexity of string motion, is it possible that the string in
>front of the plates might have sections that are moving up and down at the
>same time?  How would the transducer register this case?  If the effect is to
>average the motion over the 8 cm being measured, then it seems possible that a
>vibrating string might register 0 volts at times on the tracing.
>

Answer:


First, it does not measure the string velocity which always is changing
between two parameters.  In general the velocity of the string is near zero
when it reaches its maximum displacement.  Similarly, the velocity is at its
max when it passes its former rest position before impact.

Because the plates are long compared to the string our monochord measures
average displacement of the string by recording the voltage on the plates at
discrete time intervals.

I entered into this experiment several years ago with a physics
instrumentation specialist here at the University of Cincinnati.  My initial
objective was to measure the unstruck plane independently with the struck
plane.  The experiment led to more questions than we could answer with this
method. We discovered several interesting facets with regard to bridges.  We
are currently devising a new experiment to test our hypotheses further.  Our
goal has changed from the one stated above to that of measuring bridge
impedance in the piano as a function of frequency.

I will place some pictures of the monochord on my web site sometime within
the next few days.
****************************************************************************

Michael J. Wathen			Phone:	513-556-9565
Piano Technician			Fax:	513-556-3399
College-Consevatory of Music		Email:  Michael.Wathen@UC.Edu
University of Cincinnati
Cincinnati, OH 45221-0096

http://www.uc.edu/~wathenmj