# A train is moving on a straight track with speed 20 ms-1. It is blowing its whistle at the frequency of 1000 Hz. The Percentage change in the frequency heard by a person standing near the track as the train passes him is close to (speed of sound = 320 ms-1)

$\\\text{Before crossing the train, apparent frequency heard by the person.} \\ f_{1}=\left(\frac{c}{c-v_{s}}\right) f_{0}=\left(\frac{320}{320-20}\right) 1000\\ Similarly, apparent frequency heard, after crossing the trains \\\mathrm{f}_{2}=\left(\frac{\mathrm{c}}{\mathrm{c}+\mathrm{V}_{\mathrm{s}}}\right) \mathrm{f}_{0}=\left(\frac{320}{320+20}\right) 1000$

$\begin{array}{l} {[c=\operatorname{speed} \text { of sound }]} \\ \Delta f=f_{1}-f_{2}=\left(\frac{2 \mathrm{cv}}{c^{2}-v_{s}^{2}}\right) \times f_{0} \\ \text { or } \frac{\Delta f}{f_{0}} \times 100=\left(\frac{2 \mathrm{cv}}{c^{2}-v_{s}^{2}}\right) \times 100 \end{array}$

$\begin{array}{l} =\frac{2 \times 320 \times 20}{300 \times 340} \times 100 \\ \\ =\frac{2 \times 32 \times 20}{3 \times 34}=12.54=12 \% \end{array}$

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