1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Constructive and destructive interefernec and a pair of speakers

  1. Mar 3, 2008 #1

    TFM

    User Avatar

    [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. Mar 3, 2008 #2
    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. Mar 4, 2008 #3

    TFM

    User Avatar

    I am not sure what you mean by signal?

    TFM
     
  5. Mar 5, 2008 #4

    TFM

    User Avatar

    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. Mar 5, 2008 #5

    TFM

    User Avatar

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Constructive and destructive interefernec and a pair of speakers
Loading...