Where is the speed of sound greatest?

Sound is a pressure wave transmitted by particles pushing against their neighbors. Its speed depends on two things: how much the medium resists being compressed (its stiffness, or bulk modulus) and how much mass has to be moved (its density). The stiffer and less dense a medium is, the faster the wave travels. That's why steel, which is very stiff, carries sound at about 5,900 meters per second; water, at about 1,480; and air, which is highly compressible, at 343 meters per second at 20 °C. The intuition that dense air "conducts better" is wrong: what matters is the ratio between stiffness and density, not density alone.

In an ideal gas, stiffness and density increase together with pressure, so pressure cancels out and the speed of sound depends only on the absolute temperature and the composition of the gas. In dry air it is approximately 331 m/s at 0 °C and rises about 0.6 m/s for every degree. At 40 °C it is around 355 m/s; in the tropopause of the standard atmosphere, at 11,000 m and -56.5 °C, it drops to 295 m/s. That drop explains why an airliner cruising at 850 km/h sits at around Mach 0.8: the reference value that defines the Mach number is smaller at altitude. Composition matters too: in helium, light and monatomic, sound travels at nearly 1,000 m/s, which is why inhaling it raises the pitch of a person's voice; in sulfur hexafluoride, much heavier, it drops to about 130 m/s.

The local speed of sound sets the Mach number, and the Mach number sets the onset of shock waves, wave drag, and buffeting. The same aircraft, at the same true airspeed, is closer to the transonic regime in cold air at altitude than in warm air at sea level. That's why historic supersonic tests, such as the Bell X-1's in 1947, were carried out at high altitude: cold air lowers the speed needed to exceed Mach 1, and the lower density reduces loads on the airframe. A jet's instruments continuously calculate the Mach number from the total air temperature measured by a nose-mounted probe.

Sound also travels through the metal of the aircraft itself, and that much higher speed is the basis for ultrasonic inspection of stringers and riveted joints: an emitted pulse and its echo take microseconds to travel through the thickness of a part, and any crack reveals itself through an early reflection. In seawater, at about 1,500 m/s, maritime patrol aircraft rely on sonobuoys and sonars. So depending on where you look, the same physical phenomenon is slow in the cabin, fast in the wing, and even faster beneath the sea.