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Doppler effect: speed the source or observer needs for a given apparent frequency

This type of question, asked 2 times: 11 May 2023 S1, 25 Apr 2025 S2. All 2 questions below, oldest first.

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  1. Question 1

    11 May 2023 S1

    37
    With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?

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  2. Question 2

    25 Apr 2025 S2

    33
    At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?

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