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If the frequency of a wave is the property of the source emitting the wave, the number of times it vibrates per second, why does the frequency of an approaching or a receding ambulance or train change as observed by a stationary observer?

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The source "launches" wave fronts at a given frequency, but it launches each one from a new location. If the source is moving toward the observer, each new wave front is launched from a location closer to the observer than the last, and so takes less time to reach the observer than the previous one. So, the time between wave front arrivals at the observer is less than the time between launches.

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