Question

One mach number is equal to
A. \[1Km{{s}^{-1}}\]
B. \[1{N}/{{{m}^{2}}}\;\]
C. velocity of light
D. speed of sound

Answer 1

Hint: Mach number is the comparison of the speed of an object to the speed of the sound in a medium given by the equation, \[Mach\text{ }no=\dfrac{u}{v}\]. Mach no= 1 means the object and sound share the same speed. Speed of sound in air is considered as 1234.8 kmph

Complete Step-by-Step solution:
Fluids are forms of matter that deforms easily under continuous stress. As we know liquids, gases and plasma together form fluids. The study of the motion of these three together is known as fluid dynamics.
Mach number is usually used in fluid dynamics. It deals with the compressibility of a fluid. It is the ratio of flow velocity past a boundary to the local speed of light. Or in simple words, let us consider an aircraft is flying at an altitude ‘a’. Then Mach number is nothing but the ratio of the speed of the aircraft moving in the medium to the speed of sound in the undisturbed medium through which it is travelling.
Mach speed is considered when an object moves faster than the speed of sound. Since Mach number is the ratio between two velocities, it is a dimensionless quantity. There are some factors that affect the value of Mach number like temperature, density, altitude etc.
Mach number = speed of airplane in the medium / speed of sound in the undisturbed medium i.e.,
Mach number = \[\dfrac{u}{v}\]……….(1)
where u is the speed of the aircraft in the medium
and v is the speed of sound through the medium.
Mach numbers are widely used in order to compare the speed of the moving objects through fluids such as aircrafts. If the Mach number is one, it implies that the object is moving with speed of the sound.
One Mach number is equal to 1234.8.
By categorizing the value of Mach number, aircrafts are broadly classified into
Subsonic – Mach no<1.0 eg. Helicopter
Transonic – Mach no~1.0 eg. Civilian aircraft
Supersonic- Mach no>1.0 eg. Modern fighter aircraft, missiles
Hypersonic- Mach no >5.0 eg. Space craft
We are very familiar with all these terms.
Therefore in conclusion option D is the correct answer.

Note: Always remember Mach number is constant at a particular altitude. At higher altitude, the density of air decreases. Thus the speed of sound decreases following the increase in mach number.