For waves moving through the atmosphere at a constant velocity, higher frequency waves must have proportionally longer wavelengths. a)

Question

For waves moving through the atmosphere at a constant velocity, higher frequency waves must have proportionally longer wavelengths.
a) true
b) false

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Vân Khánh 5 years 2021-07-13T02:06:48+00:00 1 Answers 45 views 0

Answers ( )

  1. Doris
    0
    2021-07-13T02:08:01+00:00
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    Answer:

    false.

    Explanation:

    We know that for a wave that moves with velocity V, with a wavelength λ, and a frequency f, we have the relation:

    V = λ*f

    So, if the velocity is constant and we increase the frequency to:

    f’ > f

    we will have a new wavelength λ’

    Such that:

    V = f’*λ’

    And V = f*λ

    Then we have:

    f’*λ’ = f*λ

    Solvinf for λ’, we get:

    λ’ =(f/f’)*λ

    And because:

    f’ > f

    then:

    (f/f’) < 1

    Then:

    λ’ =(f/f’)*λ < λ

    So, if we increase the frequency, we need to decrease the wavelength.

    So, for higher frequency waves, we must have proportionally shorter wavelengths.

    Then we can conclude that the given statement:

    “or waves moving through the atmosphere at a constant velocity, higher frequency waves must have proportionally longer wavelengths”

    is false.

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