Question

An important news announcement is transmitted by radio waves to people who are 300 km away and sitting next to their radios, and also by sound waves to people sitting 8.00 m from the newscaster in a newsroom. What is the difference in time Δ between each group of people receiving the news?

Answer 1

The difference in time (Δ) between people receiving a news announcement via radio waves 300 km away and by sound waves 8.00 m away is approximately 0.022 seconds. This calculation is based on the speed of light for radio waves and the speed of sound in air at 20°C.

Step-by-step explanation:

To find the difference in time (Δ) between the groups receiving the news via radio waves and by sound waves, we need to consider the speed of radio waves and the speed of sound. Radio waves travel at the speed of light, which is about 300,000 km/s, while the speed of sound in air at 20°C is approximately 343 m/s.

For the radio waves:

• Distance: 300 km (300,000 m)
• Speed: 300,000 km/s (3×108 m/s)
• Time: Time = Distance / Speed = 300,000 m / 3×108 m/s = 0.001 seconds

For the sound waves:

• Distance: 8.00 m
• Speed: 343 m/s
• Time: Time = Distance / Speed = 8.00 m / 343 m/s = 0.023 seconds

Thus, the difference in time:

Δ = Time(sound waves) - Time(radio waves) = 0.023 s - 0.001 s = 0.022 seconds

Therefore, the people in the newsroom will hear the announcement approximately 0.022 seconds after the people listening to their radios 300 km away.