Question

Overtones show up at approximately which two sets of wavenumbers?

Answer 1

Overtones are frequencies higher than the fundamental frequency, with the second and third overtones showing up at frequencies that are three and four times the fundamental frequency respectively.

Step-by-step explanation:

Overtones, in the context of wave physics, refer to frequencies that are higher than the fundamental frequency of a vibrating system, such as a string or an air column in a tube. The third and fourth harmonics, also called the second and third overtones respectively, show up at wavenumbers related to the fundamental frequency (ƒ1). The wavelength of the third harmonic (second overtone) is λ3 = L and its frequency is ƒ3 = 3ƒ1, while the fourth harmonic (third overtone) has a wavelength of λ4 = ⅔ L and a frequency of ƒ4 = 4ƒ1. In general, overtones are integral multiples of the fundamental frequency.

Answer 2

Overtones occur when a vibrational frequency mode is excited from v=0 to v=2, which is called the first overtone wave number, or v=0 to v=3, the second overtone wave number.