Question

An important news announcement is transmitted by radio waves to people who are 120 km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 3.6 m from the newscaster. take the speed of sound in air to be 350 m/s. what is the difference in time that the message is received? answer in units of ms.

Answer 1

The radio waves move at the speed of light:
`c=3 \cdot 10^8 m/s`, and they cover a distance of
`S=120 km= 1.2 \cdot 10^5 m` to reach the people, so the time they take to cover this distance is

`t= (S)/(c)= (1.2 \cdot 10^5 m)/(3 \cdot 10^8 s)=4 \cdot 10^(-4) s = 0.4 ms`

Instead, the sound waves move at speed of sound: v=350 m/s and they cover a distance of S=3.6 m, so the time they take to reach the people is

`t= (S)/(v)= (3.6 m)/(350 m/s)=0.0103 s=10.3 ms`

Therefore, the difference in time between the two messages is

`\Delta t = 10.3 ms - 0.4 ms=9.9 ms`