Question

An important news announcement is transmitted by radio waves to people who are 46 km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 2.1 m from the newscaster. Take the speed of sound in air to be 348 m/s. What is the difference in time that the message is received

Answer 1

Answer:

$0.005847\ \text{s}$

Explanation:

Radio waves travel at the speed of light

$c$ = Speed of light = $3\times 10^8\ \text{m/s}$

$d_r$ = Distance between two radios = 46 km

$v$ = Speed of sound in air = 348 m/s

$d_s$ = Distance sound travels across the newsroom = 2.1 m

Time taken by the radio signal to reach the required location is

$t_r=\dfrac{d_r}{c}\\\Rightarrow t_r=\dfrac{46\times 10^3}{3\times 10^8}\\\Rightarrow t_r=0.000153\ \text{s}$

Time taken by sound to reach the required location is

$t_s=\dfrac{d_s}{v}\\\Rightarrow t_s=\dfrac{2.1}{348}\\\Rightarrow t_s=0.006\ \text{s}$

The time difference is

$t_s-t_r=0.006-0.000153=0.005847\ \text{s}$

The difference in time that the message is received is $0.005847\ \text{s}$.