Mach number is defined as the ratio of an object's speed to the speed of sound in the surrounding medium. Which option best expresses this definition?

Mach number is defined as the ratio of an object's speed to the speed of sound in the surrounding medium. Which option best expresses this definition?

• A. The ratio of air density to velocity.
• B. The ratio of velocity to the speed of light.
• C. The ratio of speed to the speed of sound.
• D. The ratio of velocity to the speed of sound in the surrounding medium.

Answer: (D)

The main idea is that Mach number measures how fast something is moving relative to the local speed of sound. It is a dimensionless quantity that compares the object's speed to how fast sound travels in the same medium and conditions. The correct expression is the object's speed divided by the speed of sound in the surrounding medium, which is v / a, where v is the velocity and a is the local speed of sound. This explicitly uses the local medium because the speed of sound changes with temperature, composition, and pressure, so the comparison must be made with the local value. Why this fits best: it directly captures the essence of Mach number as a speed ratio to the local sound speed, making the result unitless and applicable to classify flow regimes (subsonic, sonic, supersonic). The other options introduce a factor that doesn’t belong (density), or mix in an unrelated constant (speed of light), or omit the important qualifier that the speed of sound is that of the surrounding medium.

The main idea is that Mach number measures how fast something is moving relative to the local speed of sound. It is a dimensionless quantity that compares the object's speed to how fast sound travels in the same medium and conditions. The correct expression is the object's speed divided by the speed of sound in the surrounding medium, which is v / a, where v is the velocity and a is the local speed of sound. This explicitly uses the local medium because the speed of sound changes with temperature, composition, and pressure, so the comparison must be made with the local value.

Why this fits best: it directly captures the essence of Mach number as a speed ratio to the local sound speed, making the result unitless and applicable to classify flow regimes (subsonic, sonic, supersonic). The other options introduce a factor that doesn’t belong (density), or mix in an unrelated constant (speed of light), or omit the important qualifier that the speed of sound is that of the surrounding medium.