A string of length 1.0 m and mass 9.0 g is
fixed at one end to a vibrator and at the other end to a hanging mass
through a pulley, as shown in the figure. The frequency of the vibrator is
fixed at 60 Hz. Find the mass of the weight that must be hung from the
string, if it is to resonate in the second harmonic.
The resonant frequencies
are given by
Let us calculate the
speed of the wave in the case of a resonance with two loops (n = 2).
The tension
t
in the string is related to the speed of the wave through the relation
where
m is the linear mass density of
the string and m is the hanging mass.
Therefore,