UPSC Prelims 2007 Q110: Science & Technology – Physics
Assertion (A): A jet aircraft moving at Mach number equal to 1 travels faster at an altitude
of 15 km than while moving at Mach number equal to 1 near sea level.
Reason (R): The velocity of sound depends on the temperature of the surrounding medium.
- (a) Both A and R are true and R is the correct explanation of A
- (b) Both A and R are true but R is NOT the correct explanation of A
- (c) A is true but R is false
- (d) A is false but R is true
Answer: (d) A is false but R is true
Explanation
Mach number and the speed of sound
Mach 1 = the local speed of sound.
Speed of sound in air depends on temperature: v ∝ √T.
| Altitude | Temperature (standard atmosphere) | Speed of sound |
|---|---|---|
| Sea level | ~15 °C | ~340 m/s |
| 15 km | ~−56 °C | ~295 m/s |
So Mach 1 at 15 km is slower than Mach 1 at sea level.
Assertion (A): Mach 1 at 15 km is faster than at sea level — FALSE.
Reason (R): Speed of sound depends on the temperature of the medium — TRUE.
Answer: (d) A is false but R is true.
Why each option is right or wrong
- (a) Incorrect. A is false — Mach 1 is slower in the cold air at 15 km.
- (b) Incorrect. Statement A is false, so this option cannot be right.
- (c) Incorrect. A is false and R is true — the reverse of this option.
- (d) CORRECT. Cold air at altitude → lower speed of sound → Mach 1 is slower. R is the right physics.
Key point
Speed of sound ∝ √T. Colder air at 15 km → Mach 1 ≈ 295 m/s vs ≈ 340 m/s at sea level.
Remember
Mach 1 is slower at high altitude because the air is colder.
Common mistakes
- Thinking thinner air at altitude makes sound faster — pressure/density cancel out; only temperature matters for an ideal gas.
- Treating Mach 1 as a fixed speed — it depends on local conditions.
- Forgetting that temperature falls with height in the troposphere (~6.5 °C per km).
Exam tip
Sound in gases: temperature up → faster; temperature down → slower. Pressure alone → no effect.
Sources
- NCERT Class XI — Physics Part II, Ch 15 (Waves)
- NCERT Class XI — Fundamentals of Physical Geography, Ch 8 (Atmosphere)