The permanent bar magnet is moved to the left, toward a loop of wire (as shown). The north pole of the magnet is closer to the loop, as shown. What direction will the (induced) magnetic field be in the center of the loop of wire?

The direction of induced current in the coil is clockwise. Since the magnet is being moved away, the magnetic flux linked with the coil must be decreasing. hence the induced magnetic field must be in same direction as external magnetic field .

hence C is south pole and A is North Pole

Wavelength divides in half and speed stays the same.