Constructive and destructive interefernec and a pair of speakers

  1. [SOLVED] Constructive and destructive interefernec and a pair of speakers

    1. The problem statement, all variables and given/known data

    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 speakers emit sound waves that travel directly from the speaker to point Q

    What is the lowest frequency for which constructive interference occurs at point ?
    What is the lowest frequency for which destructive interference occurs at point ?


    2. Relevant equations

    not sure

    3. The attempt at a solution

    I know that constructive occurs when waves are in phase, destructive when 180 degrees/pi radians out of phase

    Any ideas would be most appreciated

    Thanks,

    TFM
     
  2. jcsd
  3. If speaker_a produces a signal sin(2*pi*f * t), what will be the signal at a point a distance d_a from a? This is just the same signal delayed by the time to get to the
    distance d_a
    This will still be a sine wave so the signal looks like sin(2*pi*f*t - .........)


    speaker_b produces the same signal, so the same applies at a distance b_d from b.

    The total signal is just the signal from both speakers added.

    d_a and d_b are given in the problem
     
  4. I am not sure what you mean by signal?

    TFM
     
  5. Constructive Interference occurs at [tex] n\lambda [/tex]

    Destructive Interference occurs at [tex] \frac{n}{2 \lambda}[/tex]

    Using the basic wave equation, speed = wavelength * frequency, they can be rearranged for frequency:

    Constructive Interference occurs at [tex] n(\frac{344}{f}) [/tex]

    Destructive Interference occurs at [tex] n(\frac{344}{2f}) [/tex]

    but I am unsure how I should proceed from now?

    (I hope this is relevant)

    Any help would be much appreciated,

    TFM
     
  6. Looked in my book, fpuind the right equation:

    constructive:

    [tex] f_n = \frac{nv}{d} [/tex]

    destructive:

    [tex] f_n = \frac{nv}{2d} [/tex]

    where d is the path difference.

    TFM
     
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