An open organ pipe emits E (330 Hz ) when the temperature is 26 ∘C. The speed of sound in air is v≈(331+0.60T)m/s, where T is the temperatur

Question

An open organ pipe emits E (330 Hz ) when the temperature is 26 ∘C. The speed of sound in air is v≈(331+0.60T)m/s, where T is the temperature in ∘C. Determine the length of the pipe.

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RobertKer 4 years 2021-08-22T17:12:24+00:00 1 Answers 34 views 0

Answers ( )

  1. minhkhang
    0
    2021-08-22T17:14:15+00:00
    Reply

    Answer:

    0.525 m

    Explanation:

    From the question,

    In an open pipe,

    v = λf………………. Equation 1

    Where v = speed of sound in the pipe, f = frequency, λ = wave length.

    But,

    λ = 2l……………. Equation 2

    Where l = length of the pipe

    Substitute equation 2 into equation 1

    v = 2lf………….. Equation 3

    make l the subject of the equation

    l = v/2f…………. Equation 4

    Given:

    v ≈ (331+0.60T) m/s at T = 26°C

    v ≈ (331+0.60×26) ≈ 346.6 m/s

    f = 330 Hz.

    Substitute these values into equation 4

    l = 346.6/(2×330)

    l = 346.6/660

    l = 0.525 m

    Hence the length of the pipe is 0.525 m

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