Why is it preferable to say that the doppler effect causes a shift in frequency rather than a shift in wavelength? I often read on websites that they define the doppler effect as a change in frequency.
The doppler shift causes a shift in wavelength at the origin of the wave (the frequency of the source never changes). This results in a shift in frequency for the observer.
In the link below you can see the emission of the wave for a moving source causes the wavelength to be shorter in front and longer behind. The actual source isn't changing in frequency. So it's a matter of relativity. To the traveling observer (in the source), only the wavelength is changing, to the stationary observer (experiencing the doppler shift) both frequency and wavelength have changed.
In case of a travelling observer , there is change in wavelength,and the magnitude and sign of change in wavelength depends on the velocity of the observer. Let's say an observer moves towards a stationary source emitting pulses with a frequency of 'f' with a velocity vo . A pulse reaches the observer and by the next time a pulse reaches the observer, the observer will have traveled a distance 'vo/f' towards the pulse. Here , relative velocity comes into picture and so the wavelength changes due to the doppler effect.