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30 June, 03:21

Consider a standing wave in a one dimensional ideal medium of length "D" (like a vibrating string).

a) how many vibration modes are possible with wavelengths between D/10 and D/20?

b) how many are possible with wavelengths between 10D and 20D?

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  1. 30 June, 03:57
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    a) 20 nodes b) zero nodes

    Explanation:

    When we have standing waves in a bend we have nodes at the ends and the equation describes the number of possible waves in the string is

    L = n λ/2

    Where λ is the wavelength, L is the length of the string, in our case it would be D and n is an entered. We can strip the wavelength of this expression

    λ = 2L / n

    Let's calculate what value of n we have for a wavelength equal to D/10

    λ = 2D / n

    λ = D / 10

    We match and calculate

    2D / n = D / 10

    2 / n = 1/10

    n = 20

    Perform them for λ = D / 20

    λ = 2D / n

    2D / n = D / 20

    n = 2 20 = 40

    Since n is an inter there should be a wavelength for each value of n in the bone period there should be 20 different wavelengths

    B) for La = 10D

    2D / n = 10D

    1 / n = 5

    n = 1/5 = 0.2

    La = 20D

    2D / n = 20D

    1 / n = 10

    n = 1/10 = 0.1

    These numbers are not entered so there can be no wave in this period
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