(1-2) ① Here is the first harmonic. There are nodes (zero amplitude) at either end, where the string is fixed, and in the exact centre where Cormorant’s wing was touching the string.
(1-2) ① Here is the first harmonic. There are nodes (zero amplitude) at either end, where the string is fixed, and in the exact centre where Cormorant’s wing was touching the string.
② The higher harmonics must all have nodes at the fixed end points but they differ by having additional nodes in between:
Because the wavelength decreases as the additional nodes are formed, each successive harmonic will sound a higher note.
③ There must be node at either end of the string because it is fixed at those positions. Nodes are formed every half a wavelength, so a standing wave can only be formed if the length of the string is a whole number multiple of the half-wavelength. In other words, if the string has length L, then Cormorant can place his wingtip at a distance of L/2 or L/3 etc from one end, and generate a standing wave. However if he places it 37% of the way along, the only way that can happen is if both the 37% on one side and the 63% on the other side both accommodate exactly a whole number of half-wavelengths. Since these numbers have no common factors other than 1, this can only be achieved by a harmonic having at least 100 half-wavelength elements. Such an extreme distortion of the string would have a negligible amplitude, so would generate, at best, a very faint sound.