Shock Waves and Sonic Boom Quiz
When a source moves through a medium faster than the local speed of sound, linear wave theory breaks down and pressure disturbances pile up into an abrupt, nearly discontinuous front called a shock wave. This quiz tests the key ideas from Lesson 14: the definition and formation of shock waves, the Mach number and its flow regimes, the geometry of the Mach cone, the origin of the sonic boom, and the practical consequences for supersonic aircraft.
What you will practise
- Recognising the supersonic regime and applying ##M = v_s / c##
- Using the Mach cone relation ##\sin\theta = \dfrac{c}{v_s} = \dfrac{1}{M}##
- Distinguishing the moving source from the stationary shock front it drags behind
- Interpreting irreversibility, entropy rise, and the Rankine–Hugoniot jumps across a front
- Applying shock wave ideas to medicine, astrophysics, and flight regulations
Work carefully with the cone-angle formula and the sound-speed relation ##c = \sqrt{\gamma R T / M}## before selecting an answer. Good luck!
Q1. A shock wave is best described as:
A shock wave is a thin transition region, typically a few mean free paths thick, across which pressure, density, temperature and entropy change almost discontinuously.
Q2. A shock wave forms whenever a disturbance moves relative to the medium:
Shock waves form when the disturbance moves supersonically relative to the medium, so pressure disturbances cannot propagate ahead of it and accumulate into an abrupt front.
Q3. The defining thermodynamic feature of a shock front is that:
The defining feature is irreversibility: entropy rises across the front, so the process cannot be reversed without external work.
Q4. The Mach number of a source is defined as:
The Mach number is ##M = v_s / c##, where ##v_s## is the source speed and ##c## the local sound speed.
Q5. According to the flow regimes described in the lesson, a Mach number of 3 corresponds to:
The supersonic band is 1.2 to 5, so ##M = 3## lies in the supersonic regime.
Q6. In the lesson, the transonic regime is identified as the band where:
The transonic region (0.8 to 1.2) is where drag rises sharply because shock formation begins on wing surfaces.
Q7. The half-angle ##\theta## of the Mach cone produced by a supersonic source satisfies:
The Mach cone geometry gives ##\sin\theta = \dfrac{c}{v_s} = \dfrac{1}{M}##.
Q8. An aircraft flies at Mach 2. The half-angle of its Mach cone is:
With ##\sin\theta = \dfrac{1}{M} = \dfrac{1}{2}##, we get ##\theta = 30^\circ##.
Q9. The sonic boom heard on the ground is correctly explained as:
The sonic boom is not a single event but a carpet of pressure signatures traced along the ground; the sharp crack arises from the abrupt shock front.
Q10. Why does the sonic boom arrive as a sharp crack rather than a gradual rumble?
The boom is sharp because the shock front is an abrupt, nearly discontinuous pressure jump, unlike smoothly radiating subsonic wavefronts.
Q11. For an ideal gas, the speed of sound is given by:
In an ideal gas, ##c = \sqrt{\gamma R T / M}##, which for air at sea level gives approximately ##340\ \text{m s}^{-1}##.
Q12. As the absolute temperature of air rises, the speed of sound:
Sound speed in air rises with the square root of absolute temperature, from about ##295\ \text{m/s}## at ##216\ \text{K}## to about ##340\ \text{m/s}## at ##288\ \text{K}##.
Q13. A common error that JEE questions test is:
Misapplying the Doppler expression to a supersonic source is a common error; candidates must first recognise which regime applies.
Q14. Across the bow shock of an aircraft at Mach 2, the lesson states that pressure ratios can:
A supersonic aircraft at Mach 2 compresses air across its bow shock in microseconds, producing pressure ratios that can exceed 2:1 and temperature jumps of several hundred kelvin.
Q15. Which statement about subsonic versus supersonic sources is correct?
Subsonic sources produce spherical wavefronts that spread apart; supersonic sources produce wavefronts that pile up along a common envelope.