Question

Question: The frequency of a steam train whistle as it approaches you is 565 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?

Short answer

The velocity of the train is \(26\;{\rm{m/s}}\).

Step-by-step solution

Determination of speed of train

For a moving object, the hearing frequency depends upon the velocities of the object and the velocity of sound. This effect is known as Doppler’s shift. The equations are different in conditions when objects move toward each other and away from each other.

Given Information

Given data:

The frequency of train whistle is \({f_{approach}} = 565\;Hz\).

The frequency of train whistle when it has passed through is \({f_{recede}} = 486\;Hz\).

Find the velocity of the train

The observed frequency is given by the equation:

As the train is going beyond the person, then

Equate the observed frequency when train is approaching and train is receding.

Thus, the velocity of the train is \(26\;{\rm{m/s}}\).