A surfer is actually traveling on which part of a surface wave

Surfer travels at the crest

Explanation:

Waves on the surface of water is known as surface waves in which the disturbance will travel in form of crest and trough.

Now we know that disturbance or energy will travel along the surface due to which the crest and trough will also move along the surface with same speed

Now here surfer travel at the position of the crest of the wave because at that position the surfer will remain at the top of the wave due to which his balancing while he is in motion will be easier.

So here we can say the surfer will remain static with respect to the crest of the wave and crest move with the speed of wave and hence A surfer is actually traveling on CREST of a surface wave

A surfer travels on the crest of a surface wave