An important news announcement is transmitted by radio waves to people sitting next to their radios 73 km from the station and by sound waves to people sitting across the newsroom 2.90 m from the newscaster. Taking the speed of sound in air to be 343 m/s, who receives the news first?
Question
An important news announcement is transmitted by radio waves to people sitting next to their radios 73 km from the station and by sound waves to people sitting across the newsroom 2.90 m from the newscaster. Taking the speed of sound in air to be 343 m/s, who receives the news first?
Solution
To answer this question, we need to calculate the time it takes for the radio waves and sound waves to reach the listeners.
- Calculate the time it takes for the radio waves to reach the listeners 73 km away.
Radio waves travel at the speed of light, which is approximately 3.00 x 10^8 m/s.
Time = Distance / Speed
Time = 73,000 m / 3.00 x 10^8 m/s = 0.000243 seconds
- Calculate the time it takes for the sound waves to reach the listeners 2.90 m away.
Sound waves travel at the speed of 343 m/s.
Time = Distance / Speed
Time = 2.90 m / 343 m/s = 0.00845 seconds
Comparing the two times, the people sitting across the newsroom 2.90 m from the newscaster receive the news first because sound waves reach them in 0.00845 seconds, which is faster than the 0.000243 seconds it takes for the radio waves to reach the listeners 73 km away.
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