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Home/ Questions/32. Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal...
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James Portman
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James Portman
Asked: April 13, 20222022-04-13T09:34:57+00:00 2022-04-13T09:34:57+00:00In: Advanced-Physics

32. Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal…

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32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal...

32. Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speak- ers emit sound waves that travel directly from the speaker to point Q. (see figure) (a) What is the lowest frequency for which constructive interference occurs at point Q? (b) What is the lowest frequency for which destructive interference occurs at point Q? 2.00 m
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  1. William Roberts
    2022-04-13T12:52:12+00:00Added an answer on April 13, 2022 at 12:52 pm

    (a)

    Constructive interference occurs when the path difference between 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal... and n=1,2,3…

    Path difference between the points Q of the speakers A andB = 3 m-1 m = 2m

    Therefore, n HTML0$ = 2 (or) = (2/n)

    We know that Frequency (f), = Velocity(v) / Wavelength( 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal...

    Velocity of sound waves in air (v), = 344 m/s

    Substituting 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal... for v in equation (1)

    f = (344m/sxn) / 2m = 172Hz xn where n=1,2,3 …..

    The lowest frequency at which constructive
    interference takes place at at the point Q is 172 Hz
    is the result.

    (b)

    When the path difference between 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal... and n/2 is greater than , destructive interference occurs.

    Path difference between the points Q of the speakers A andB = 3 m-1 m = 2m

    Thus, n/2x = 2m (or = 4 / n).

    Substituting 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal... for v in equation (1)

    f = (344m/sx n)/ 4m = 86Hz x N where n=1,3,5 …..

    Therefore, the lowest frequency at which destructive
    interference takes place at the point Q is 86 Hz

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