For both sound waves and light waves, as the observer starts moving towards the wave source, the frequency increases and the wavelength decreases so that their product, the speed of the wave, can gloriously remain the same, Divine Einstein, yes we all believe in relativity, relativity, relativity:
http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Doppler_Nav.swf "INTRODUCTION: Our ears detect changes in the frequency of sound waves due to the Doppler shift, but the waves change in another way, too: in their wavelength. Wavelength and frequency are closely related: if one increases, the other decreases. Their product, the speed of the wave, remains the same. The spaceship in this interactive has an instrument which detects electromagnetic radiation. You can see the wavelength and frequency change as the ship and the source of radiation move through space. EXERCISES: 2. Now click on the "Observer Approaches" button. The ship will start flying towards the source. What is the wavelength of the waves now, as the ship approaches the source? Does the frequency increase or decrease? SOLUTIONS: 2. The wavelength shrinks so that about three waves now fit within the graph. (...) The frequency increases."
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang_observed/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)."
http://www.imcce.fr/en/grandpublic/systeme/promenade/pages3/327.html "Décalage d'un spectre : l'effet Doppler. Cet effet se manifeste lorsque l'onde émise et l'observateur sont en mouvement l'un par rapport à l'autre et dans la direction de propagation de l'onde. L'observateur à l'arrêt voit passer 2 maxima consécutifs à chaque intervalle de temps t. S'il s'approche de la source de rayonnement, ce temps sera plus court. L'onde se manifestera avec une fréquence plus élevée, DONC UNE LONGUEUR D'ONDE PLUS COURTE."