Final answer:
The fundamental frequency of a guitar string will be 2.5 times the original frequency if its length is reduced to 40% of the original, as wave speed remains constant and frequency must inversely compensate for the change in string length.
Step-by-step explanation:
The fundamental frequency of a guitar string when it is fingered at a length of only 40% of its original length will be 2.5 times the original frequency. As the length of the string is directly proportional to the wavelength, when the string length is shortened, the wavelength also shortens. According to the wave equation v = f λ, where v is the wave speed, f is the frequency, and λ is the wavelength, if the speed of the wave remains constant, decreasing the length (and hence the wavelength) of the string by a factor of 0.4 (or 40%) means that the frequency must increase by a factor of 1/0.4 to keep the equation balanced, resulting in the frequency being 2.5 times the original frequency.