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16 November, 19:26

A person stands 6.00 m from a speaker, and 8.00 m from an identical speaker. What is the wavelength of the first (n=1) interference maximum (destructive)

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  1. 16 November, 20:07
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    wavelength = 4 m

    Explanation:

    For distance 6 and 8m and speed of sound in air = c.

    The travel time form the various distances 6 and 8 are 6/c and 8/c respectively.

    cos (wt1) + cos (wt2) = 0

    for a shift in phase t1 = t - 6/c,

    t2 = t - 8/c

    substituting t1 and t2

    cos (π - w (t - 8/c)) = cos (w (t - 6/c))

    solving using trigonometry identities in radians.

    we have,

    π - 2πn = w (t - 8/c) - w (t - 6/c)

    putting w = 2πf

    π - 2πn = 2πf (t - 8/c) - 2πf (t - 6/c)

    dividing both sides by π

    1 - 2n = 2ft - 16 (f/c) - 2ft + 12 (f/c)

    simplifying we have,

    1 - 2n = - 4 (f/c)

    solving for f we have,

    f = c/4 (2n - 1)

    putting n=1 and c = 343m/s

    f = (343/4) * (2 (1) - 1)

    f = 85.75 Hertz

    wave lenght = c/f, where c = speed of sound in air, f = frequency

    wave lenght = 343/85.75 = 4m
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