In this case we are confronted
with a system that presents several resonances corresponding to the
vibration modes of a string fixed at its two ends where a standing wave
is formed. The fundamental mode is resonant at a frequency given by f
0 =v/(2L), v being the velocity of the waves in the string of
L. The other higher order modes resonate at frequencies given by nf
0 , n=2,3,4...
The three experiments we have
ready to launch have been built on a string composed by 21 particles
charge=0) linked by springs (k=50000, default length 10). The end
are fixed. The period for the fundamental mode (free-undamped) has been
measured to be 9.3906.
Excitation of the different modes
In all experiments we have
included an extra particle (big mass = 10000, q=100), to visualize the
Electric field value that will produce the external force on selected
particles of the string.
It is highly recommended to
have a look to the space distribution of the different modes previously
presented (Section 3.3), because it is the base to feed a given mode.
To excite a mode we observe
where are its crests located. There we introduce charges to be driven
an external Electric field. This field is set to a frequency close to
resonance frequency of the mode we want to excite.
To excite the fundamental
mode (with a maximum amplitude, crest, at the center), the particle at
this point has been given a charge (q=10000)
The alternating Electric
field amplitude is Ez = 20, Period =9.3906.
For this mode (with
two crests and a valley at the center), the particles number 5, from
and from right, are given equal and opposite charges (of magnitude
The frequency of the
alternating field is set to twice the value of the frequency
to the fundamental mode (Period T= 4.7)
The third higher
mode is excited by reducing the period to 1/3 the value corresponding
fundamental mode of vibration (T= 3.13).
To excite this mode,
a charge at the center of the string is enough, like for the
mode. The difference between both cases is the frequency.
- Reload the last experiment (Mode 3)
Change the electric
field Period to 3 times the present value and observe/explain the
- Reload the same experiment and set the
field Period to the one corresponding to the 2nd. mode (T=4.7).
- Try to excite the mode number 5.