Longitudinal Wave
A longitudinal wave makes the medium vibrate back and forth along the direction the wave travels, forming compressions and rarefactions.
Definition
A longitudinal wave pushes and pulls in the same direction it travels, squeezing the medium together and spreading it apart over and over as the wave passes, with regions of squeezed particles called compressions and spread-out regions called rarefactions; one wavelength is the distance from one compression to the next. Sound waves in air and seismic P-waves are longitudinal, and because every material resists being squeezed, longitudinal waves can travel through gases, liquids, and solids. The displacement $s(x,t) = s_{\max}\cos(kx - \omega t)$ produces a pressure variation $\Delta P = -B\,\partial s/\partial x$ that is $90^\circ$ out of phase with displacement, so pressure peaks where displacement is zero, and wave speed depends on the medium's stiffness and density, $v = \sqrt{B/\rho}$ for fluids and $v = \sqrt{Y/\rho}$ for thin solid rods, with $B$ the bulk modulus and $Y$ Young's modulus.
Example
Push and pull one end of a stretched slinky and bunched-up coils travel down it followed by stretched-out sections; a tuning fork vibrating at $256\ \text{Hz}$ in air at $343\ \text{m/s}$ produces compressions $\lambda = v/f = 343/256 \approx 1.34\ \text{m}$ apart. Water, with $B = 2.2 \times 10^9\ \text{Pa}$ and $\rho = 1000\ \text{kg/m}^3$, carries sound at $v = \sqrt{2.2 \times 10^6} \approx 1{,}480\ \text{m/s}$, over four times its speed in air, while steel ($Y = 2.0 \times 10^{11}$, $\rho = 7{,}850$) carries it at about $5{,}050\ \text{m/s}$, which is why an approaching train can be heard through the rails before it is heard through the air.
Key Insight
Sound is a longitudinal wave: a voice squeezes and stretches the air in front of it, and those squeezes travel to someone's ear, which is also why sound can be heard underwater and through walls, since every material resists compression. Sound in air is fast not because air is stiff but because it is light; the ratio $B/\rho$ is what matters, and helium's low density is why sound moves faster in it and voices sound higher.