How Do You Convert Mach to m/s?
Multiply the Mach number by 343 to get meters per second at sea level. The formula is: m/s = Mach x 343. Since the speed of sound at 20 degrees C in dry air is exactly 343.0 m/s, the Mach number is simply the ratio v/343.
Tom Brewer demonstrates shockwave physics to Maya. A bullet at Mach 2.5 travels at 2.5 x 343 = 857.5 m/s. At this speed, the bullet creates a Mach cone with a half-angle of arcsin(1/2.5) = 23.6 degrees. The shockwave reaches a person 100 meters away about 0.3 seconds after the bullet passes.
Speed of Sound in Different Conditions
| Condition | Speed of Sound (m/s) | Mach 2 Equivalent (m/s) |
|---|---|---|
| Air at -40 degrees C | 307 m/s | 614 m/s |
| Air at 0 degrees C | 331 m/s | 662 m/s |
| Air at 20 degrees C (standard) | 343 m/s | 686 m/s |
| Air at 35 degrees C | 352 m/s | 704 m/s |
| Helium | 1,007 m/s | 2,014 m/s |
| Water (25 degrees C) | 1,497 m/s | 2,994 m/s |
| Aluminum | 6,420 m/s | 12,840 m/s |
| Diamond | 12,000 m/s | 24,000 m/s |
Practical Applications
Lightning Distance Estimation
Coach Rivera teaches his team about lightning safety. Sound travels at 343 m/s (Mach 1 by definition). If thunder arrives 5 seconds after the flash, the lightning was 343 x 5 = 1,715 meters = 1.7 km away. He tells his team to seek shelter when the gap drops below 10 seconds (3.4 km), per safety guidelines.
Supersonic Projectile Testing
Dana Kowalski observes a ballistic test. The projectile exits at Mach 3.2 = 1,097.6 m/s. Traveling 50 meters to the target takes 50 / 1,097.6 = 0.0456 seconds. The high-speed camera records at 100,000 fps, capturing 4,556 frames during the projectile flight. Each frame shows the projectile advancing 0.011 meters (11 mm).
Earthquake Wave Speed
Maya studies seismic waves. P-waves travel through rock at about 6,000 m/s = Mach 17.5 in air-equivalent terms. S-waves are slower at about 3,500 m/s = Mach 10.2. The time delay between P and S wave arrival helps seismologists determine earthquake distance: each second of delay represents about 8 km of distance from the epicenter.