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.

Example 1

The hanging mass is kg.

Answer

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,