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Every so often, you might hear somebody mention that something or other has reached supersonic speeds. Obviously that must be pretty fast, but exactly how fast is it?
Let’s start with same basic terminology. Most people use the word “speed” to describe how fast something is moving. However, in physics, speed is just part of the story. The direction of movement is also crucial in most physics calculations. Scientists use the term “velocity” to describe both the magnitude (or speed) of your movement combined with the direction.
The final term we need to understand to talk about supersonic speed is something called the Mach number. The Mach number is the ratio of the velocity of an object relative to some medium and the speed of sound in that medium.
Let’s look at an example. According to the IAAF, world record holder Usain Bolt can run at a maximum velocity of 12.27 meters per second (m/s). The speed of sound is around 340.3 m/s (technically the speed of sound varies somewhat with temperature, but we’ll just stick with this number to make things easier). If you take the ratio of these two numbers, 12.27 m/s divided by 340.3 m/s, you get 0.036. In other words, Usain Bolt can run at Mach 0.036.
Those of you who have been listening to the Math Dude podcast and are good with fractions will notice that as Usain’s velocity increases, the ratio of his velocity to the speed of sound approaches 1. If he were able to run at 340.3 m/s, he would reach Mach 1.