A string vibrating at its fundamental frequency f1 is made to take up the next two standing wave patterns. What frequencies are those?

1. The overtones, also called harmonics, are whole-number multiples of the fundamental frequency. 2. The next pattern up fits one more half wavelength on the string, halving the wavelength and doubling the frequency, so f_2 = 2 f_1. 3. The one after that gives f_3 = 3 f_1, and the pattern continues. 4. Fractions of the fundamental would need wavelengths longer than 2L, which cannot fit between two fixed ends. 5. Squared multiples such as 4 and 9 belong to no standing wave pattern on a string. _Source: OpenStax College Physics (CC BY 4.0), Ch 16 "Oscillatory Motion and Waves", section Standing Waves_