With both ends of the cord fixed one obtains the next-to-lowest possible
frequency (second harmonic)
when, besides the
nodes
at the end of the cord,
appears a node in the middle of the cord.
This frequency must be such that the space between the two ends of the cord,
 ,
corresponds to the wavelength,
=λ.
Since the speed of waves in the cord, v,
is supposed to be constant, one has
v = f × λ
→
f = v /
= 2v / 2
Remember that,
although you do not observe waves moving,
the standing wave is the result of the constructive interference
of many waves which all the time
reflect at the ends of the cord.
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