Do we really experience the Doppler effect at a railway station?

Photo by Stefan Stefancik

Everyone who has studied physics in high school knows the doppler effect. For those who don't, the doppler effect is an effect when there is a relative motion between a source of a wave and an observer.

As a result of this relative motion, the wave's frequency differs from the actual frequency (f).

This is called the Doppler Effect and the observed frequency(f') can be calculated using the following basic equations.

Where

•  V is the speed of the wave in the medium;
•  Vo is the speed of the observer
•  Vs is the speed of the source 

Now it's time to get into the topic.

Some people think that we experience the doppler effect when a source reaches us or leaves us at a constant speed. For instance, they think the change in the sound we experience when a train comes toward us is a result of the doppler effect.

This is a half-truth. 

According to the above basic formula, we can derive a new formula to calculate the observed frequency of the train's sound. But that changed frequency is a constant as the train comes toward us at a constant speed. So, we cannot observe a change in frequency.

But we know we can observe a change in sound. 

what is that change?

It is the intensity of the sound. The intensity is defined as the amount of energy that flows in a specific area in a time unit.

We can calculate the intensity of the sound using the following equation.

According to the above equation, you can see the intensity of the sound is when the train comes towards you because the r is decreased with time. As our ears are sensitive to the intensity of the sound, we experience a change.

When the train leaves you, the r is increased and the I is decreased so we observe a change in the sound.

But wait, you can experience a true result of the doppler effect at the railway station when the train passes you. Before passing you, it was coming toward you so the f' is calculated as shown below.

After passing you the formula is changed and you can calculate the new frequency (f'") using the following formula.

So when the train passes you, you will experience a change in the frequency (delta f) as a result o the doppler effect.

delta f is calculated as shown below.

But if the V>>>vs the difference of the frequencies becomes too small.

Hope you learned something new!.

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