Question

A train, blowing a whistle of frequency f, is standing in the railway yard. A person is running towards the engine. The frequency of the sound of the whistle as heard by the person will be
1) Greater than f
2) Less than f
3) Equal to f
4) Greater or less than f depending on the speed of the train

Answer 1

Hint:Whenever a car approaches a person he hears the sound of the car increasing as the car is moving towards him and as the car goes away from the person the sound of the car fades away. This phenomenon is known as Doppler shift. Here the person is running towards the engine, to find out the frequency of the sound of the whistle the person hears apply the concept of Doppler’s shift.

Formula used:
\[f' = f(\dfrac{{v + {v_o}}}{v})\];
Here:
\[f'\]= Observed frequency of sound.
\[f\]= Original frequency of sound.
\[v\]= Velocity of sound in air.
\[{v_o}\]= velocity of Observer.

Complete step-by-step answer:
Analyze the formula and deduce the answer:
\[f' = f(\dfrac{{v + {v_o}}}{v})\];
In the above formula we can see that the observed frequency \[f'\]is the multiplication of the original frequency \[f\]and the combination of the two velocities that is the velocity of sound in air v and the velocity of the observer\[{v_o}\]. Here from the given equation one can deduce that the observed frequency \[f'\] is greater than the original frequency\[f\]. As the observed frequency is the multiplication of the original frequency and the sum of two velocities it is more than obvious that the observed frequency is greater than the original frequency.

Final Answer:Option “1” is correct. The frequency of the sound of the whistle as heard by the person will be greater than f. (\[f'\]>\[f\])

Note:The question is based upon the Doppler shift which is given by the formula\[f' = f(\dfrac{{v + {v_o}}}{v})\]. Here one has to analyze the formula and come to a conclusion that the observed frequency is greater than the original frequency. It is counter intuitive to observe that the person is hearing a sound of greater frequency than the original frequency of the train. It is important to do the analysis based on the formula.