I believe you are correct: the frequency at which a thing vibrates is considered a constant, e.g. a tuning fork set to “A” will still vibrate at “A” whether on Earth, on Mars, or in a vacuum. The pitch will go unchanged in this case. Given the relationship of velocity, frequency, and wavelength (v = fw, where “v” is velocity, “f” is frequency, and “w” is wavelength), the wavelength would actually shrink if the velocity is reduced.
NASA has an excellent page with audio samples demonstrating both this and the incredibly quick drop-off effect on higher frequencies in low atmo, found here.
