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Closed pipe partly filled with water: new frequency of a given harmonic

This type of question, asked 3 times: 25 Apr 2025 S1, 13 May 2026 S1, 15 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    25 Apr 2025 S1

    35
    The fundamental frequency of a closed pipe is 400 Hz. If (13)rd\left( \frac{1}{3} \right)^{rd} length of the pipe is filled with water, the frequency of the 2nd 2^{\text{nd~}} harmonic of the pipe will be (Neglect end correction)

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  2. Question 2

    13 May 2026 S1

    121
    The fundamental frequency of a closed pipe is 400400 Hz. If 13rd\dfrac{1}{3}^{rd} pipe is filled with water then the frequency of 3rd3^{rd} harmonic of the pipe will be (Neglect end correction)

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  3. Question 3

    15 May 2026 S2

    123
    In an experiment with a closed organ pipe, it is filled with water by (15)th\left(\dfrac{1}{5}\right)^{th} of its volume. The frequency of the fundamental note will change by

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