Question

please solve with this formulafo = [ v / v – vs ] x fs3.The railroad crossing lights turn red, so McKayla and her sister must stop and wait for the train to pass by. As they wait, McKayla's sister Kylie grabs her phone and uses an app to measure the frequency of the approaching train's horn. The app reads 429 Hz. Assuming the train's original horn frequency is 400 Hz and the speed of sound is 330 m/s, how fast is the train going in m/s and miles per hour?

Answer 1

rearrangesAnswer:

Explanation:

For an approaching train with velocity vs, the observed frequency fo is

$f_o=\frac{v_{\text{sound}}}{v_{\text{sound}}-v_{\text{train}}}f_{\text{source}}$

Now we know that

$\begin{gathered} f_o=429hz \\ f_{\text{source}}=400hz \\ v_{\text{sound}}=330m/s \\ v_{\text{train}}=\text{?} \end{gathered}$

therefore, we have

$429=\frac{330}{330-v_{\text{train}}}\cdot400$

dividing both sides by 400 gives

$\frac{429}{400}=\frac{330}{330-v_{\text{train}}}$

which rearragnes to give

$\frac{429}{400}\cdot(330-v_{\text{train}})=330$$\Rightarrow330-v_{\text{train}}=330\cdot\frac{400}{429}$$v_{\text{train}}=330-330\cdot\frac{400}{429}$$v_{\text{train}}=\frac{290}{13}$$\boxed{v_{\text{train}}=22.31m/s}$

which in miles per hour is

$\boxed{v_{\text{train}}=50\text{mph}}$