A vibrating string has infinitely many resonant frequencies

Evidence

The infinitely growing complexity of mass-spring systems is understood when analysing the behaviour of a vibrating string, such as the guitar string, supported at both ends. Figure 2.7 illustrates the eight lowest modes of such a string. We can consider the string as a continuum of infinitely small masses and springs. This means that, in theory, there are infinitely many modal frequencies (see also Sections 2. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 171