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22 September, 09:24

Which sets of data show a wave with the shortest wavelength? A. Speed=100 million m/s and frequency = 50 million Hz. B. Speed=150 million m/s and frequency=1500 Hz C. Speed=300 million m/s and frequency = 100 Hz

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  1. 22 September, 12:01
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    The answer is A. Speed=100 million m/s and frequency = 50 million Hz.

    Let's calculate for each choice the wavelength using the equation:

    v = f * λ ⇒ λ = v : f

    where:

    v - the speed,

    f - the frequency,

    λ - the wavelength.

    A:

    v = 100 000 000 m/s

    f = 50 000 000 Hz = 50 000 000 1/s (Since f = 1/T, so units are Hz = 1/s)

    ⇒ λ = 100 000 000 : 50 000 000 = 2 m

    B:

    v = 150 000 000 m/s

    f = 1 500 Hz = 1 500 1/s

    ⇒ λ = 150 000 000 m/s : 1 500 = 100 000 m

    B:

    v = 300 000 000 m/s

    f = 100 Hz = 100 1/s

    ⇒ λ = 300 000 000 m/s : 100 = 3 000 000 m

    According to these calculations, the shortest wavelength is needed for choice A.
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