To calculate the wavelength of a standing wave on an open string, you need to consider the length of the string and the mode of the standing wave.
The fundamental frequency (first harmonic) is the lowest frequency at which a standing wave can occur on a string. In this mode, the string vibrates as a whole, creating a single antinode in the center and nodes at each end. The wavelength of the fundamental frequency on an open string is equal to twice the length of the string:
λ = 2L
where λ represents the wavelength and L represents the length of the string.
For higher harmonics (modes), the standing waves on the string have additional nodes and antinodes. The wavelengths of these higher harmonics are related to the fundamental wavelength by the following equation:
λn = λ1/n
where λn represents the wavelength of the nth harmonic and n is the mode number. The mode number n indicates the number of nodes or antinodes present on the string. The fundamental mode has n = 1, the first overtone has n = 2, the second overtone has n = 3, and so on.
To calculate the wavelength of a specific mode on an open string, you can use the above equation with the fundamental wavelength (λ1) determined by the length of the string.