The Problem:
Here is an extract from the diary of Samuel Pepys for 4 June 1666, written in London. ‘We find the Duke at St James’s, whither he is lately gone to lodge. So walking through the Parke we saw hundreds of people listening to hear the guns.’ These guns were at the battle of the English fleet against the Dutch off the Kent coast, a distance of between 110 and 120 km away. The speed of sound in air is 344 m sTM. How long did it take the sound of the gunfire to reach London?
Step 1: Convert distance to meters
We are given:
- Distance: Between 110 km and 120 km,
- Speed of sound in air: 344 m/s.
Convert distances to meters:
- 110 km = 110,000 m,
- 120 km = 120,000 m.
Step 2: Calculate time using the formula
Time = Distance / Speed
- For 110,000 m: Time = 110,000 / 344 ≈ 319.77 seconds,
- For 120,000 m: Time = 120,000 / 344 ≈ 348.84 seconds.
Step 3: Convert time to minutes
- 319.77 seconds ≈ 5.33 minutes,
- 348.84 seconds ≈ 5.81 minutes.
Final Answer:
The sound of the gunfire took between 5.33 minutes and 5.81 minutes to reach London.
