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Mach Number Calculator

Compare object speed to local sound speed (subsonic / sonic / supersonic)

Parameters

m/sⓘ
m/sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Mach Number:
1.17;1.17;

Examples

Supersonic jet

v = 686 m/s, v_s = 343 m/s.

    Subsonic aircraft

    v = 250 m/s.

      Visualization

      Mach Number — Comparing Speed to Sound Speed

      The Mach number Ma = v/v_s is a dimensionless ratio of the speed of an object (or flow) v to the local speed of sound v_s in the surrounding medium. It tells whether disturbances (sound waves) can outrun the object.

      Subsonic (Ma < 1): the object moves slower than sound. Pressure disturbances propagate ahead, warning the medium. Air flows smoothly in many cases; wings and cars often operate subsonically.

      Sonic (Ma = 1): object speed equals sound speed. Drag rises sharply in the transonic regime (Ma ≈ 0.8–1.2) due to shock formation and wave drag. “Breaking the sound barrier” means crossing Ma = 1.

      Supersonic (Ma > 1): the object outruns its sound waves. A Mach cone forms; shock waves produce sudden pressure jumps. A sonic boom is heard when shock waves from a supersonic aircraft reach the ground.

      Sound speed in an ideal gas: v_s = √(γRT/M), where γ ≈ 1.4 for air, R is gas constant, T is absolute temperature (K), M is molar mass. At 20°C (293 K), v_s ≈ 343 m/s in dry air. Hotter air → faster sound → higher v_s.

      Example: jet at v = 686 m/s in air with v_s = 343 m/s → Ma = 2 (supersonic). Concorde cruised at Ma ≈ 2. Fighter aircraft exceed Ma 2; spacecraft re-entry reaches Ma > 20 in the atmosphere.

      Mach number differs from Doppler effect: Doppler shifts observed frequency when source and observer move relative to each other; Mach number compares source speed to v_s in the medium. Class 12 Doppler; engineering uses Ma for aerodynamics.

      Key Concepts

      • Ma = v/v_s
      • Subsonic Ma < 1
      • Sonic Ma = 1
      • Supersonic Ma > 1
      • v_s ≈ 343 m/s at 20°C in air
      • v_s = √(γRT/M) ideal gas

      Real-World Applications

      • Aircraft, missile, and spacecraft aerodynamics
      • Wind tunnel and CFD Mach scaling
      • Sonic boom and supersonic transport
      • Astrophysical shocks (supernova, bow shocks)
      • Class 12–JEE Mach and Doppler concepts

      Explore Further

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      Physics Equations

      Mach Number:
      Ma=vvsMa = \frac{v}{v_s}

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Mach Number

      Equation:

      Ma=vvsMa = \frac{v}{v_s}

      Explanation:

      Ratio of object speed to local sound speed.

      2

      Step 2: Given

      Result:

      v=400m/s,vs=343m/sv = 400 m/s, vₛ = 343 m/s
      3

      Step 3: Calculate

      Calculation:

      Ma=400343=1.1662Ma = \frac{400}{343} = 1.1662

      Result:

      Ma=1.1662Ma = 1.1662
      4

      Step 4: Regime

      Supersonic — shock waves form

      Explanation:

      At Ma = 1, sound and object move together.

      5

      Step 5: Doppler Connection

      High Ma implies strong compression (bow shock) and sonic boom when Ma crosses 1.

      Explanation:

      Sound speed depends on medium temperature.

      6

      Step 6: Typical vₛ

      Air at 20°C: vₛ ≈ 343 m/s

      Explanation:

      vₛ = √(γRT/M) for ideal gas.

      Frequently Asked Questions (FAQ)

      What causes a sonic boom?

      Shock waves from supersonic flight merge into a N-wave pressure pulse heard on the ground when the aircraft is at suitable altitude and speed.

      Mach number in water?

      Use v_s ≈ 1500 m/s. A torpedo at 30 m/s has Ma ≈ 0.02 — still subsonic in water.

      Is Ma the same as speed?

      No. Ma depends on both v and local v_s (temperature, medium). Same v gives different Ma in hot vs cold air.

      Hypersonic?

      Often Ma > 5. Extreme heating and dissociation of air; re-entry vehicles face this regime.

      Relation to Doppler?

      Doppler: observer hears shifted f when source moves. Mach: ratio v/v_s in medium; sonic boom is shock physics, not simple Doppler.

      Practice MCQs

      1. Mach number:
      2. Ma = 2 means:
      3. v_s in air ~
      4. Sonic flight Ma:
      5. Shock waves when:
      6. Higher temperature air:

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