For all the allowed vibration(s) (wavelength(s)) of a plucked guitar string, what is the correct relationship between the length of the string, L, and the wavelength, λ?
A)L = λ/2
B)L = λ
C)L = nλ/2 where n is a positive integer
D)L = nλ where n is a positive integer
E)L = 1/λ

Question

Quizplus · Accepted Answer

The correct relationship for the allowed vibrations of a plucked guitar string is L = nλ/2, where n is a positive integer. This formula represents the fundamental frequency and its harmonics, with n=1 being the fundamental frequency, n=2 the first overtone, and so on. This relationship arises because the string supports standing waves that have nodes at both ends, and the length of the string is equal to an integer multiple of half wavelengths.

For All the Allowed Vibration(s) (Wavelength(s)) of a Plucked Guitar