Chapter 22, Problem 40GP

To determine

To Calculate: Time lag.

Answer to Problem 40GP

  $1.35s$

Explanation of Solution

Given info:

Distance from radio, $d_{radio}=3.84\times {10}^{8}m$

Distance from sound, ${\text{d}}_{\text{sound}}=25\text{m}$

Factor, $c=3.00\times {10}^{8}m/s$

Speed of sound, $v_{sound}=343m/s$

Formula used:

To calculate the total time, sum up the time taken by radio and time taken by sound.

Distance is rate times time. So, formula to calculate time: $\Delta t=\frac{d}{c}$

Where,

  $\Delta t$ is time

  $d$ is distance

  $c$ is a factor

Calculation:

According to the question,

  $t=t_{radio}+t_{sound}$

  $t=\left(\frac{d_{radio}}{c}\right)+\left(\frac{d_{sound}}{v_{sound}}\right)$

Substitute the given values in formula, $t=\left(\frac{d_{radio}}{c}\right)+\left(\frac{d_{sound}}{v_{sound}}\right)$

  $t=\left(\frac{3.84\times {10}^{8}m}{3.0\times {10}^{8}m/s}\right)+\left(\frac{25m}{343m/s}\right)$

  $t=1.35s$

Conclusion: The required time is $1.35s$ .