NDA (I) 2017 General Ability Test · Question 55 of 149

Correct — A, supersonic. The Mach number of a body is the ratio of its speed to the speed of sound in the medium it is moving through, so a Mach number greater than one simply means the body is outrunning the sound waves in that medium — the definition of supersonic flight. Because the disturbance the body creates can no longer race ahead of it, the pressure waves pile up into a shock cone that trails behind, and an observer on the ground hears it pass as a sonic boom. Note that the Mach number is a ratio and not a fixed speed, so the same Mach 1 corresponds to different speeds at different temperatures.

• (b)subsonic — Subsonic is the opposite case, a Mach number less than one, where the body moves more slowly than sound in the medium and the pressure waves it makes can still run ahead of it.
• (c)300 m/s — This is a single fixed speed, and a Mach number cannot be converted into one without knowing the medium and its temperature. It is also close to the speed of sound in air near the ground, so it corresponds to roughly Mach 1 rather than to a speed comfortably above it.
• (d)about 10 m/s — Ten metres per second is about thirty-six kilometres an hour, some thirty times slower than sound in air. That is deeply subsonic, a Mach number of roughly 0.03.

The Mach number, named after Ernst Mach, is the dimensionless ratio of the speed of an object to the local speed of sound. Flight regimes are named from it — subsonic below Mach 1, transonic around Mach 1, supersonic above Mach 1 and hypersonic from about Mach 5 upward. Since the speed of sound in a gas depends on its temperature, the actual speed represented by Mach 1 falls as the air gets colder with altitude.

The trap in this item is the pair of numerical options, which invite you to convert a ratio into a speed. Resist it — without a stated medium and temperature no number is right. The physics worth carrying away is that the speed of sound in dry air is about 331 metres per second at 0 degrees Celsius and rises by roughly 0.6 metres per second for each degree of warming, so an aircraft holding Mach 1 in the cold air at high altitude is actually flying slower than an aircraft holding Mach 1 near the ground. UPSC set exactly that point as an assertion-reason item in 2007.

• Mach number is the ratio of the speed of a body to the speed of sound in the surrounding medium, and it has no units.
• A Mach number above one is supersonic, below one is subsonic, near one is transonic and about five or more is hypersonic.
• The speed of sound in dry air is roughly 331 metres per second at 0 degrees Celsius and increases as the air gets warmer.
• Because the speed of sound falls with temperature, Mach 1 corresponds to a lower ground speed at high altitude than at sea level.
• A body moving faster than sound trails a shock cone, heard on the ground as a sonic boom.

• Treating Mach 1 as a fixed number of metres per second — it changes with the medium and its temperature.
• Assuming sound travels fastest in air; it is fastest in solids and slowest in gases.
• Confusing supersonic with ultrasonic — ultrasonic describes a frequency above human hearing, not a speed.

NDA asks for the flight regime named by a Mach number, or tests the temperature dependence of the speed of sound that lies behind it.

• practice — not a real PYQ

  An aircraft flying at Mach 0.8 is described as

  • (a)supersonic
  • (b)subsonic
  • (c)hypersonic
  • (d)stationary

  Answer(b) subsonic — a Mach number below one means the aircraft is slower than sound in the surrounding air.

• practice — not a real PYQ

  The speed of sound in air increases when

  • (a)the temperature of the air rises
  • (b)the temperature of the air falls
  • (c)the frequency of the sound rises
  • (d)the loudness of the sound rises

  Answer(a) the temperature of the air rises — the speed of sound in a gas grows with its temperature and does not depend on frequency or loudness.