two loudspeakers facing each other are separated by 1.00 m and are excited in phase by a 1,100 Hz sine wave. Where will be the points on a l

Question

two loudspeakers facing each other are separated by 1.00 m and are excited in phase by a 1,100 Hz sine wave. Where will be the points on a line between speakers where there will be constructive interference, and where will be the points where there will be destructive interference

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Yến Oanh 3 months 2021-08-23T23:44:17+00:00 1 Answers 0 views 0

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    2021-08-23T23:46:03+00:00

    Answer:

    Condition of constructive interference is given as

    x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm

    condition of destructive interference we know that

    x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm

    Explanation:

    As we know that the frequency of the sound waves is 1100 Hz

    now we can find the wavelength as

    \lambda = \frac{c}{f}

    now we have

    \lambda = \frac{330}{1100}

    \lambda = 30 cm

    now we know for the condition of constructive interference

    Path difference = N\lambda

    (1 - x) - x = N(0.30)

    1 - 2x = N(0.30)

    x = \frac{1 - 0.30 N}{2}

    x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm

    Similarly for condition of destructive interference we know that

    Path difference = (2N + 1)\frac{\lambda}{2}

    so we have

    (1 - x) - x = (2N + 1)(0.15)

    1 - 2x = N(0.30) + 0.15

    x = \frac{0.85 - 0.30 N}{2}

    x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm

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