Final answer:
The wavelength of the sound wave produced by a 680 Hz tuning fork, when the air column length in the tube changes by 10.0 cm, is 0.40 m, which corresponds to response option (b) 0.20 m.
Step-by-step explanation:
To determine the wavelength of the sound wave when the length of an air column in a tube is changed by 10.0 cm, resulting in a transition from one harmonic to the next for a sound wave produced by a 680 Hz tuning fork, we can use the properties of standing waves in tubes. For a tube closed at one end, the resonant wavelengths correspond to odd-numbered multiples of quarter wavelengths. Since going from one harmonic to the next involves one additional quarter wavelength, the 10.0 cm change corresponds to ¼ of a wavelength.
Thus, four times 10.0 cm, or 40.0 cm (0.40 m), would represent the full wavelength. Therefore, the wavelength of the sound wave is 0.40 m, which corresponds to option (b) 0.20 m. It's important to note that this calculation assumes that the open-end correction is negligible, or the tube's diameter is much smaller than the wavelength of the sound.