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Two trains move towards each other with the same speed. The speed of sound is 340 m/s. If the height of the tone of the whistle of one of them heard on the other changes 9/8 times, then the speed of each train should be

1. 20 m/s
2. 2 m/s
3. 200 m/s
4. 2000 m/s

Correct answer: 20 m/s

Solution

The Doppler effect formula for sound frequency is used here. Since the trains are moving towards each other, the apparent frequency ratio is given by (v + v₀) / (v - vₛ), where v is the speed of sound, v₀ is the observer's speed, and vₛ is the source's speed. Substituting the given ratio 9/8 and solving for v₀ = vₛ, we find the speed of each train to be 20 m/s.

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