(Eq. ) -
The speed at which waves travel down the string (defined presently as
the ratio of the wavelength 
to the period T of a standing
wave) has the value 
. We find this result by just
rearranging the equation of motion for the string into the standard
wave equation form. This result for the wave speed has a very
interesting similarity with the equation for the natural frequency of
a harmonic oscillator 
. In both cases the
quantity which measures how quickly things happen in the system (the
wave speed v for the string and the natural frequency 
for the oscillator) being equal to the square-root of the ratio
between something measuring the tightness of the restoring forces in
the system (the tension 
in the case of the string and the
spring constant k in the case of the oscillator) and something else
measuring the inertia in the system (the mass per unit length 
for the string and the mass m for the oscillator). In both cases,
it makes sense that the strength of the restoring forces appears on
top (so that stronger forces lead to quicker responses) and that the
inertia appears on the bottom (so that heavier systems respond more slowly).