Final answer:
The wavelength of the constituent traveling waves on a 40-cm string vibrating in its fundamental mode is 80 cm. Therefore, the correct option is C.
Step-by-step explanation:
When a string is vibrating in its fundamental standing wave mode, the wavelength of the constituent traveling waves is related to the length of the string. In this mode, the string resembles half of a wave with a node at one end and an antinode at the other. Therefore, the string length is equal to half of the wavelength of the wave. In the case of the 40-cm long string, since the string is half the wavelength, the wavelength is 80 cm (Option C).
To determine the wavelength of the standing wave, we need to consider the length of the string and the mode of vibration. In the fundamental mode, the string forms a half-wavelength. Since the length of the string is given as 40 cm, the wavelength of the fundamental standing wave is 2 times the length, which is 80 cm. Therefore, the correct option is C.