Final answer:
Higher harmonics in standing waves on a string fixed at both ends have shorter wavelengths and higher frequencies; the frequency of each harmonic is a multiple of the fundamental frequency.
Step-by-step explanation:
The general pattern that holds for various excited states in standing waves on a rope or string fixed at both ends is that higher harmonics have shorter wavelengths. This can be understood by considering that the length of the string only supports waves that fit a whole number of half-wavelengths between the fixed ends. As we increase the harmonic number, which implies an increase in the number of half-wavelengths (nodes), the wavelength must decrease to fit within the same string length. Moreover, since the wave speed remains constant for a given medium and tension, the frequency, which is the wave speed divided by the wavelength, must increase with the harmonic number. Thus, higher harmonics have higher frequencies, and this is described by the relationship fn = n*ƒ1, where fn is the frequency of the nth harmonic and ƒ1 is the fundamental frequency.