Mersenne’s Speed of Sound

The flash is seen immediately. The boom takes time to reach the ear.

How far is the cannon? 1200 m

From 1200 m away, you’d hear the bang after 3.50 s.

Cannon formula: v = d / Δt

Distance d (m) Time Δt (s)

Speed: — m/s

The sound travels to the wall and back to the ear.

How far is the wall? 85 m

The sound goes to the wall and back. You’d hear the echo after 0.50 s.

Echo formula: v = 2d / Δt

Distance d (m) Time Δt (s)

Speed: — m/s

In the 1630s, Marin Mersenne compared the instant flash from a cannon to the delayed “bang” to estimate how fast sound travels.

He also timed echoes from distant walls. Because an echo travels to the wall and back, the sound covers twice the measured distance.

Formulas:

Cannon: v = d / Δt Echo: v = 2d / Δt

Here, v is speed in meters per second, d is distance in meters, and Δt is time in seconds.

This activity uses: v = 343 m/s, a useful classroom value for air near 20 °C.

In real life, temperature and humidity change the speed slightly. A simple temperature model is v ≈ 331 + 0.6T m/s.