What Is the Mach Number (And What Mach Is the Speed of Light)?

In the simplest of terms, the Mach number is a representation of one’s speed in relation to the speed of sound. In other words, it is a ratio of the velocity of an object when compared to the speed of sound within that same environment.

Because the speed of sound changes depending on the medium through which it travels, the temperature of that medium, and many other variables, the Mach number is not a definite number, but a ratio used for relative comparison for any object in motion.

Mach 1 is also known as (or equivalent to) the sound barrier. When any object reaches and then surpasses the sound barrier (which means it is now traveling faster than the sound it is creating), it creates a phenomenon known as a sonic boom. This is when all the sound waves created by the object compress together, so it arrives to the listener all at once, sounding like a loud boom.

How to Calculate Mach Number

Calculating the Mach number of any object is simple as long as you know the speed at which the object is traveling, and the speed sound travels in that same environment.

Use this equation. Where u is the speed of your object (in any terms of velocity), and c is the speed of sound in that medium (in the same terms of velocity).

With this equation, you can see that equal values in the numerator and denominator (meaning your object is traveling the same speed as sound in the same medium) give you a value of one, or Mach 1. So, if an object is traveling at twice the speed of sound in that medium, then it would have a value of Mach 2, and so on.

The Mach number is simple division. So, if you are using miles as your measure of speed, to calculate your approximate Mach number is to divide your miles per hour by 767.26 (the speed of sound in air at sea level in miles per hour).

Why the Name Mach?

Ernst Mach was an influential scientist in the nineteenth century. He conducted important work in the area of shock waves, and the behavior of light in different media. Additionally, he published important information about his observations of objects traveling at supersonic speeds.

Swiss aeronautical engineer, Jakob Ackeret, one of the most influential aviation experts of the 20th century, proposed the use of Mach’s name as the measurement of the Mach number. This was done as a tribute to Ernst Mach’s contribution to aeronautics.

When Is It Used, How Useful Is It?

Though we can use the Mach number to measure the speed of any object or vehicle through any medium, we typically use it in aviation for vehicles traveling through the air. This is because it is more useful to measure a vehicle’s speed in units that are both accurate and comprehensible. Vehicles in aviation can more easily approach speeds that we can measure in terms of the speed of sound. Miles-per-hour does not translate very well to our intuition of travel through air.

Land vehicles do not regularly approach these speeds, so we use a lower unit of speed (miles, kilometers, etc.). Famous exceptions to this include vehicles that are built to break land speed records. These vehicles regularly approach and surpass Mach 1.

Nautical vehicles calculate their speed using knots. This is useful in the Ocean where a vehicle’s surroundings are in constant motion. Due to the resistance and friction inherent in water travel, these vehicles do not approach Mach 1.

The Mach number cannot be used in space. Since sound does not travel through space, it is impossible to calculate the Mach number.

How to Use Mach Number Correctly

It is important to understand that the Mach number is a relative measure of speed. It is not an absolute unit of velocity or distance.

When calculating the Mach number, make sure you use the speed of sound within a similar medium. For example, though an object might travel at 500 miles per hour on Earth and Mars, the Mach number in each location will be different.

It is also best to use the Mach number for objects or vehicles that travel at speeds that make sense to translate into a Mach number. It is not very helpful to describe the speed of a dog in terms of Mach, for instance.

When using the Mach number, it is important to remember that the number follows the unit of measure. (Mach 1, not 1 Mach).

What Mach Is the Speed of Light?

The speed of light is a universal constant. This means that although light may appear to move slower, or propagate more slowly through different states of matter, it does not. It is always traveling at the same speed of 670,616,629 miles per hour, or c.

Using our equation to calculate the Mach number of the speed of light, we get Mach 874,030.49.

As we can see, using Mach to calculate anything relative to the speed of light is beyond reasonable comprehension or comparison. We usually only use the speed of light with anything related to stellar and interstellar sciences and subatomic colliders.

Comparable Speeds of Popular Objects

Commercial Airliner

The Boeing 747 can reach a cruise speed of 559 miles per hour, which is equal to Mach 0.85.

Space Shuttle

During takeoff, the space shuttle needed to reach a speed of 18,000 miles per hour in order to enter a stable orbit around the Earth. This is equivalent to Mach 23.4.

It began reentry into Earth’s atmosphere at an altitude of 400,000 feet. It normally reentered at speeds over 19,000 miles per hour, or Mach 25.

Bullets

The maximum speed (muzzle velocity) an average rifle bullet can reach is around 1,700 miles per hour. Equivalent to Mach 2.2.

Whips

The whip was one of the first man-made objects to break the sound barrier. The end of the whip can reach speeds in excess of 1,434 miles per hour, or Mach 1.8. The classic crack you hear while using a whip is actually a miniature sonic boom produced by the whip itself breaking the sound barrier.