Question

Unless specifically stated otherwise, you may assume the speed of sound for all the scenarios below is 350 m/s.4.A train in France is travelling west at 36.0 m/s when it blows it’s whistle. The whistle has a known frequency of 12,000 Hz. What frequency would an observer hear if she were on an eastbound train travelling towards the westbound train at 28.0 m/s?

Answer 1

In order to calculate the observed frequency, we can use the formula for Doppler's effect:

`f^(\prime)=f(v\pm v_o)/(v\pm v_s)`

Where f' is the observed frequency, f is the actual frequency, v is the speed of sound, vo is the observer speed and vs is the source speed.

Since the trains are approaching each other, the signal in the numerator is positive and the signal in the denominator is negative.

So we have:

`\begin{gathered} f^(\prime)=12000\cdot(350+28)/(350-36)\\ \\ f^(\prime)=12000\cdot(378)/(314)\\ \\ f^(\prime)=14445.86\text{ Hz} \end{gathered}`

Therefore the observed frequency is 14445.86 Hz.