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27 August, 06:56

You are using a tuning fork of frequency 320 Hz. For one particular water level, you hear a loud sound when the fork is struck and positioned just above the open end of the tube. When the water level is lowered by 535 mm, you again hear a loud sound. What is the wavelength of the 320 Hz sound waves in the column of air

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  1. 27 August, 07:47
    0
    The wavelength of the 320 Hz sound waves in the column of air is 1070 mm.

    Explanation:

    To solve the question, we note that the tube acts as a pipe with one end closed and that a stationary wave is formed in the tube from the top, to the bottom of the tube and back.

    The simplest and the first wave form in the tube has length L = Lambda/4

    That is, a node at the closed end and an antinode at the open end

    The second stationary wave is given by

    l + 535 mm = 3/4*lambda

    However v = f*lambda

    f = v/lambda = v / (4l)

    Therefore

    Lambda/4 + 535 mm = 3/4lambda

    Or 535 mm = 3/4lambda - Lambda/4 = lambda/2

    Therefore, lambda = 2*535 mm = 1070 mm

    The wavelength = 1070 mm
  2. 27 August, 08:50
    0
    Ln = 1/4 * (2n + 1) λ

    where,

    n = 0, 1, 2, 3, 4, ...,

    Ln = the length which is defined to be the distance measured from the open end of the tube to the water surface.

    Ln = 1/4 * (2n + 1) λ

    at n = 0,

    L0 = 1/4 * λ

    at n = 1,

    L1 = 3/4 * λ

    L1 - L0 = 1/2 * λ

    535 * 2 = λ

    λ = 1.07 m
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