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Two trains are traveling on the same track and in the same direction. The first train, which is behind the second train, blows a horn whose frequency is 269 Hz. The second train detects a frequency of 290 Hz. If the speed of the second train is 13.7 m/s, what is the speed of the first train?

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Answer:

37.545 m/s

Explanation:

f' = Actual frequency of horn = 269 Hz

f = Observed frequency of horn = 290 Hz

v = Speed of sound in air = 343 m/s

[tex]v_0[/tex] = Speed of second train = 13.7 m/s

[tex]v_s[/tex] = Speed of first train

From Doppler effect we have

[tex]f=f'\dfrac{v-v_0}{v-v_s}\\\Rightarrow v_s=v-\dfrac{f'}{f}(v-v_0)\\\Rightarrow v_s=343-\dfrac{269}{290}(343-13.7)\\\Rightarrow v_s=37.545\ m/s[/tex]

The speed of the first train is 37.545 m/s

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