Youare on a train travelling northat 80.0m/s relative to the ground. The air is still relativetothegroundwhen you hear the whistle of atraintravellingsouth. You know that train whistles are emitted with a frequency of 262Hz, but the whistle appears to have a frequency of 350Hz. What is the speed of the other train?

To solve this problem we will apply the concepts related to the Doppler effect. This is understood as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. Mathematically this is given as,

Here,

v = Speed of the waves in the middle

= Speed of the receiver in relation to the medium (Positive if the receiver is moving towards the transmitter or vice versa)

= Speed of the source with respect to the medium (Positive if the source moves away from the receiver or vice versa)

Our values are given as,

Replacing,

Solving for the velocity of the source,

Therefore the speed of the other train is 26.1m/s

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