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18 August, 00:36

You have an open air column of length 1.40 m in air at 24.2 °C. What is the frequency of the third harmonic?

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  1. 18 August, 02:26
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    f₃ = 371.35 Hz

    Explanation:

    First we need to find the speed o sound at given 24.2°C. For that purpose, we use the formula:

    v = v₀√ (T/T₀)

    where,

    v = speed of sound at 24.2° C = ?

    v₀ = velocity of sound at 0° C = 331 m/s

    T = Given Temperature = 24.2° C + 273 = 297.2 k

    T₀ = Reference Temperature = 0° C + 273 = 273 k

    Therefore,

    v = (331 m/s) √ (297.2 k/273 k)

    v = 345.36 m/s

    Now, for the third harmonic in the open air column:

    λ₃ = (2/3) L

    where,

    λ₃ = wavelength = ?

    L = Length of open air column = 1.4 m

    Therefore,

    λ₃ = (2/3) (1.4 m)

    λ₃ = 0.93 m

    So, for the frequency of the third harmonic, we use the formula:

    v = f₃ λ₃

    f₃ = v/λ₃

    where,

    f₃ = frequency of third harmonic = ?

    v = speed of sound at that temperature = 345.36 m/s

    λ₃ = wavelength of third harmonic = 0.93 m

    Therefore,

    f₃ = (345.36 m/s) / 0.93 m

    f₃ = 371.35 Hz
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