Work Step by Step
It is very important to look at Figure 21.5 when answering this question. The fundamental frequency of vibration for a string occurs when the only two nodes are at the endpoints. This is illustrated in the top diagram in that figure. If you lightly touch the midpoint, you impose a node there. The string no longer vibrates at the old fundamental frequency, and now vibrates in two segments, as shown in the second diagram in Figure 21.5. The frequency of the second harmonic is twice the frequency of the fundamental. (Why? The wave speed stays the same, and is equal to (wavelength)(frequency). The wavelength is divided by 2, so the frequency increases by a factor of 2.