A 64.0 cm long cord is vibrating in such a manner that it forms a standing wave with two antinodes. (The cord is fixed at both ends.) Which

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A 64.0 cm long cord is vibrating in such a manner that it forms a standing wave with two antinodes. (The cord is fixed at both ends.) Which harmonic does this wave represent

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Thu Thảo 3 years 2021-09-03T05:42:16+00:00 1 Answers 2 views 0

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  1. Verity
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    2021-09-03T05:43:58+00:00
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    Answer:

    the wave represents the second harmonic.

    Explanation:

    Given;

    length of the cord, L = 64 cm

    The first harmonic of a cord fixed at both ends is given as;

    f_o = \frac{V}{2L}

    The wavelength of a standing wave with two antinodes is calculated as follows;

    L = N—> A —–> N    +   N —-> A —–> N

    Where;

    N is node

    A is antinode

    L = N—> A —–> N    +   N —-> A —–> N =  λ/2  + λ/2

    L = λ

    The harmonic is calculated as;

    f = \frac{V}{\lambda} \\\\f = \frac{V}{L} = 2(\frac{V}{2L} ) = 2(f_o) = 2^{nd} \ harmonic

    Therefore, the wave represents the second harmonic.

    L = λ

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