A travelling wave transfers energy from place to place without transferring matter. The particles of the medium only oscillate about fixed positions. In a transverse wave they oscillate at right angles to the direction of energy transfer. In a longitudinal wave they oscillate parallel to it, making compressions (high pressure) and rarefactions (low pressure).
Sound is a longitudinal mechanical wave, so it needs a medium. Electromagnetic waves are transverse oscillations of electric and magnetic fields. They need no medium and all travel at 3.0 × 108 m s−1 in a vacuum.
Read wave graphs with care. A displacement–distance graph shows the wavelength. A displacement–time graph shows the period of one point.