Question

One Mach number is equal to
A. Velocity of light
B. Velocity of sound ($332\, m/sec$)
C. $1\, km/sec$
D. $1\, m/sec$

Answer 1

Hint:The Mach number is the ratio of speed of the object in a given medium to the speed of sound in that medium. Substitute Mach number equal to 1 in the relation for Mach number and see what you get.

Complete answer:
The Mach number is the term used to define the speed of an object with respect to speed of sound. It is the ratio of speed of the object in a given medium to the speed of sound in that medium. Therefore, we can express the Mach number as,
\[M = \dfrac{u}{v}\]
Here, u is the speed of the object in the given medium and v is the speed of sound in the undisturbed medium.
If the Mach number is 1, the above relation will becomes,
\[u = v\]
Therefore, we can say the speed of the object will be equal to the speed of sound (332 m/s).

So, the correct answer is option B.

Additional information:
The mass number can be used to express the speed of sound. If the Mach number is less than 0.8, the speed of sound is termed as subsonic, if the Mach number is 1, then the speed of sound is termed as sonic and if the Mach number is greater than 1.3 to 5, then the speed of sound is termed as supersonic. We categorize the aircraft depending on their speeds with respect to the speed of sound. For commercial aircrafts, the Mach number is less than 0.8 and their speeds are referred to as subsonic. For modern fighter aircrafts and missiles, the Mach number is greater than 1.3.

Note:The Mach number is the ratio of speed of object in a medium to the speed of sound in the same medium and not the speed of sound in air. Therefore, the Mach number depends both on the speed of the object and speed of sound in that medium. When we move high in the atmosphere, the density of the atmosphere decreases following the speed of sound also decreases.