Question

The Mach number is defined as:
A) the ratio of the stress to the strain.
B) the ratio of the strain to the stress.
C) the ratio of the speed of sound to the velocity of an object.
D) the ratio of the velocity of an object to the speed of sound.

Answer 1

Hint: The Mach number is employed in determining the velocity of an aircraft in terms of the speed of sound.

Complete step by step answer.
Step 1: Define the Mach number and discuss its significance.
Mach number is defined as the ratio of flow velocity past a boundary to the local speed of sound. In other words, it describes the velocity of an object in a fluid medium with respect to the speed of sound in the same fluid medium. As it is a ratio of speeds, it is a dimensionless quantity. If the Mach number of an object is known, then its velocity is easily understood.
The formula for Mach number is given as, $M = \dfrac{u}{c}$ where $M$ is the Mach number, $u$ is the local flow velocity with respect to the boundaries, and $c$ denotes the speed of sound in the medium.
At Mach $M = 1$, $u = c$ , i.e., the velocity of the object in the medium (local flow velocity) will be equal to the speed of sound in the same medium. At $M = 0.65$ , $u$ is 65% of the speed of sound. This regime is termed as subsonic. At $M = 1.35$ , $u$ is 35% faster than the speed of sound. This regime is termed as supersonic.
Therefore, the Mach number is defined as the ratio of the velocity of an object to the speed of sound.

Additional information: The Mach number is considered as a critical parameter while describing the motion of fluids of high speeds. The Mach number is named after Ernst Mach, an Austrian physicist, and philosopher, who was known for his study of shock waves.

Note: The speed of sound refers to the speed of sound waves. The two main factors that affect the speed of sound are the medium in which sound travels (eg; air, water) and the temperature. At higher temperatures, the molecules have more energy and vibrate faster. Thus, sound waves will propagate faster.