Sound interference

  1. Given for the problem:
    A speaker sends out two sound waves with equal Amplitudes but the frequencies are f(1) and f(2) respectively. The motion of sound as w = A * cos(k*x - t*(Omega)). The wave number's and the angular frequency's definition are the same for light.

    Find for the problem:
    Show that at a distance x directly in front of the speaker, there is destructive interference between the waves with a frequency f(1) - f(2).

    My solution so far:
    w(1) = A * cos((2PI/(Lambda(1))) * x - (2PI * f(1) * t)
    w(2) = A * cos((2PI/(Lambda(2))) * x - (2PI * f(2) * t)

    I assume that the final equation will be in the form of:
    dt = (x / v) - t
    where v is the speed of sound

    A little advice please!
     
  2. jcsd
  3. I hope i put this in the right section... It is a Sophmre level physics class... :blushing:
     
  4. Hint: You are looking for a point, x, where the two waves are out of phase by pi radians.

    -Dan
     
  5. lightgrav

    lightgrav 1,230
    Homework Helper

    "Destructive Interference" in this case is time-dependent cancellation of the total amplitude (that means add the wave functions), at any location.
    This is in contrast to location-dependent cancellation of the total amplitude
    (an interference pattern) at all time.

    Choose an x-value, and add the wave forms ; see when (time) they cancel.
     
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