Chapter 12, Problem 81GP

To determine

To Find: The speed of train.

Answer to Problem 81GP

The speed of the train is $17.4\text{m/s}$ .

Explanation of Solution

Given:

The frequency of whistles as the train approaches, $f_1=538Hz$

The frequency of train when it passes, $f_2=486Hz$

Formula used:

Write the expression for the apparent frequency.

  $f\text{'}=\frac{v}{v-v_s}f$

  $v_s$ is the velocity of the train.

  $v=343m/s$

In the first case the train is approaching and in the second case the train is leaving.

  $\begin{array}{l}case1:\\ 538=\frac{343}{343-v_s}f\mathrm{...........................}(1)\\ case2:\\ 486=\frac{343}{343+v_s}f\mathrm{...........................}(2)\end{array}$

Calculation:

Divide the equation (1) by (2):

  $\frac{538}{486}=\frac{343+v_s}{343-v_s}$

On solving,

  $\begin{array}{l}1.107(343-v_s)=343+v_s\\ 379.7-1.107v_s=343+v_s\\ 36.7=2.107v_s\\ v_s=\frac{36.7}{2.107}=17.42\text{m/s}\end{array}$

Conclusion:

The speed of the train is $17.4\text{m/s}$ .