Re: How can I measure the vibrations of a ball hitting a tennis racquet?

First of all I refer you to the book titled "The Physics of Sports."  Many
experiments like the one you wish to do are described there.  Measuring the
vibration of the strings may be a little difficult.  It might be easier to
measure the vibration of the tennis racquet itself with a video camera.  Align
your tennis racquet in your vise parallel to the ground and project the tennis
ball.  Attach a stiff piece of whatever you can find to the very top of the
raquet head. (see Fig 1 below).  With a ruler and a video camera you can record
the oscillation of the racquet.  The racquet's vibration will dampen very
quickly oscillating smaller and smaller with each period.  But if you can
measure the time it takes for the racquet to return the center on the way back
up you will have measured one HALF period of oscillation.  The frequency can be
expressed as simply 1/(FULL period).  If you can see a full swing
(down-turn-up-turn-down-center-) you might get a more accurate measurement.  I
would not expect you to be able to get better than about 20% accuracy on this. 
If you have access to a video camera and can set up a stop watch to start when
the ball is released you can measure the time it takes the ball to hit the
racquet and the oscillation of the racquet pretty easily.  You can repeat this
measurement as many times as possible to get a better idea of the true answer
(This is called signal averaging).

Measuring the vibration of the strings might be possible without hi-tech
electronic gizmo called a transducer.  A transducer is a device that coverts
mechanical motion into electrical voltage (and/or vice versa).  Transducers can
be very sophisticated but they are all basically the same idea.  Below I
describe a very crude sort of transducer using magnets instead of the usual
piezoelectric transducer elements common to such devices like radio speakers.

  A simple way might involve using magnetic induction to pick
up the movement of the strings.  Place a few small magnets aligned the same way
along the length of a given string.  Hopefully this won't change the
characteristic response of the string to much.  Anyway, if you run a several
loops of a continuous wire around the frame of the racquet head to form a coil
and attach that an oscillascope with a video camera aimed at it, you may be able
to pick up the voltage induced in the your coil due to the moving smaller
magnets.  This could give you the vibration of the string relative to the
racquet itself.

You probably need some help setting either or both of these experiments up.  And
you might even come up with a better way to it than I have designed here.  I
have a lot of experience in experimental physics and one thing always seems to
be true:  It is rare that an experiment is as easy to do as it sounds!  Good
Luck.

FIG 1:
                          %%%       +
-----------             %%%%%%      +
|  Vise    |***********%%%%%%%% --->+ruler
-----------             %%%%%%      +
                          %%%       +

FIG 2:

(racquet)
          %%%%%%%%%%%%
         %             %
        %                %
        %-----------------%%%%%%%%%%%%%%%%%
        %                %
         %             %
          %%%%%%%%%%%%


          %%%%%%%%%%%%
         %             %
        %                %%%%%%%%%%%%%%  (lead 1 to scope)  
        %   (loop of wire = coil)
        %                %%%%%%%%%%%%%%%  (lead 2 to scope)
         %             %
          %%%%%%%%%%%%





put magnets along string denoted -----
and wind coil around frame of racquet head and attach to scope

Sincerely,

Tom Cull