Is it better to call the doppler effect a change in wavelength or frequency? 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.   
 A: 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.

 Lookang, Wikimedia commons. More simulations and applets here.
A: For waves that are carried by a medium (sound waves, ocean waves, ...) one has to distinguish two cases

*

*fixed source, moving observer : the wavelength is unchanged, but for the moving observer, the frequency is different because in his point of view, the velocity of the waves is not the true one.


*moving source, fixed observer :  the wavelength is different, and the frequency is also different, since the velocity of the wave is the same.
The exact expression of the Doppler shift in terms of the velocity and the speed of the moving "partner" is not the same. I'm giving the expression for the frequency $\nu$ in terms of the original $\nu_0$ for speed $v$ of the moving partner and velocity $V$ of the wave
-Fixed source

*

*observer moving towards the source $$\nu=\nu_0\  {\frac {V+v} V}$$

*observer moving away from the source, $v\le V$ $$\nu=\nu_0\  {\frac {V-v} V}$$

*observer moving away from the source, $v\ge V$ $$\nu=\nu_0\  {\frac {v-V} V}$$
provided the source has started emitting long enough before the observer overtakes it, and the observer has not yet reached the first wave emitted by the source

Wavelength unchanged
-Fixed observer

*

*source moving towards the observer $v\lt V$ $$\nu=\nu_0\  {\frac V {V-v} }$$

*observer moving away from the source,   $$\nu=\nu_0\  {\frac V {V+v} }$$
If the source moves towards the observer with $v\ge V$, the wave has not had time to reach the observer yet.
In all cases the wavelength is $V/\nu$. (Sorry that the character $\nu$ for frequency is so close to $v$.   ;)   )
The situation is different for light. The speed of light is always the same. The changes in frequency and wavelength are always reciprocal. But the expression of the Doppler shift in special relativity is still a third one !
For light, the velocity of which is always $c$, relativity tells us it does not matter which moves and which is fixed

*

*observer and source getting closer $$\nu=\nu_0 \sqrt {\frac {c+v}{c-v}}$$

*observer and source getting further away $$\nu=\nu_0 \sqrt {\frac {c-v}{c+v}}$$
In both case the wavelength is $c/\nu$
In the case where $v$ is  much smaller than $V$ (or $c$ !!) the three expressions for the frequency are very close, whether for source and observer getting closer or farther. Wavelength, on the other hand, changes in the same way for light and fixed observer, but of course does not change at all for fixed source.
Hence it is better to think in terms of frequency. For $v$  much smaller than $V$, the relative variation ${\frac {\Delta \nu } \nu}= {\frac \nu{\nu_0}}-1$ is always very close to $v/V$ for getting closer and $-v/V$ for getting farther. For light $V=c$.
A: 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.
A: The wavelength does not change but the relative velocity of sound changes so the frequency changes. When an object is moving, the velocity of the sound wave from the object is different for the observer and it is not anymore 330 m/s.
