Question

An important news announcement is transmitted by radio waves to people who are 100km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 3.0m from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.

Answer 1

Answer on Question #52056 | Mechanics

An important news announcement is transmitted by radio waves to people who are 100 km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 3.0 m from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.

Solution

The speed of radio wave is $c = 3 \times 10^{8} \, \text{m/s}$. The speed of sound $v = 343 \, \text{m/s}$. For transmission by radio waves we obtain:

$$t_r = \frac{l_r}{c} = \frac{10^5}{3 \times 10^8} \, s \approx 3.34 \times 10^{-4} \, s$$

And for transmission by sound waves we obtain:

$$t_s = \frac{l_s}{v} = \frac{3}{343} \, s \approx 8.7 \times 10^{-3} \, s$$

Answer: $t_s > t_r$. It means that news transmitted by radio waves receives first.

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