Image 1 Caption: An animation dynamically illustrating the first 6 normal modes of standing waves on a vibrating string with fixed endpoints.
Features:
This is because a wavelength is by definition a full spatial cycle of the wave phenomenon. Usually a spatial cycle can be characterized as an up-and-down cycle.
This definition of wavelength is the useful one for analysis of wave phenomenon.
If we drive a vibrating string
with a vibrating machine
at exactly a resonance frequency f_n
(which we explain below),
we get standing waves
with exactly n anti-nodes.
What if we drive the
vibrating string
off all
resonance frequencies?
We get small
traveling waves that
varied in time.
For off resonance frequencies,
the pulls on the vibrating string
strongly cancel instead of adding up.
Now when you strike a vibrating string,
you simultaneously excite
standing waves
with multiple
superimposed resonance frequencies,
but other
frequency
waves are strongly
suppressed by canceling pulls.
L
n = --- , where L is the length of the vibrating string.
λ/2
Thus, the wavelength formula is
L
λ = ----- = 2L/n ,
(n/2)
where the first version makes sense since there are
2
anti-nodes per
standing wave.
Now we have a general formula
for phase velocity
(the velocity at which
traveling waves propagate):
phase velocity formula fλ=v ,
where v is the
phase velocity
and f is frequency).
Using this formula,
we find the resonance frequency
formula for
a vibrating string to be
f_n = n[v/(2L)] .
Online Tone Generator
for
any sound
frequency.
Turn the
sound intensity
slider
on the left way down:
e.g., ≤ 3 % for high frequency;
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To hear
Concert A 440 Hz
with overtones
for a violin
(much more pleasant than the pure
frequency
Concert A),
see
File:A440 violin.mid,
but it's probably just a
synthesizer
violin.