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Math Help - frequency

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    Unhappy Please help!

    Two point-source loudspeakers are a certain distance apart, and a person stands 12.0 m in front of one of them on a line perpendicular to the baseline of the speakers. If the speakers emit identical 1000.0-Hz tones, what is their minimum nonzero separation so that the observer hears little or no sound? (Take the speed to be exactly 340 m/s.)
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    Quote Originally Posted by pocahontas
    Two point-source loudspeakers are a certain distance apart, and a person stands 12.0 m in front of one of them on a line perpendicular to the baseline of the speakers. If the speakers emit identical 1000.0-Hz tones, what is their minimum nonzero separation so that the observer hears little or no sound? (Take the speed to be exactly 340 m/s.)
    The key to this one is that the observer needs to be standing at a point of total destructive interference. That is, the difference in the path length of the person to speaker A and the person to speaker B must be 1/2 wavelength.

    So say the person is standing in front of speaker A. Call the distance between the speakers d and the distance from the person to each speaker a and b, respectively. These three distances make a right triangle. We know a = 12.0 m and we know b - a = 1/2 wavelength. (We know it is this and not a multiple of 1/2 lambda because we are looking for the minimum separation of the speakers.) From this you should be able to construct a value for b and thus, since you have a right triangle, figure a value for d.

    -Dan
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