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Power of a sound source

  1. Jun 6, 2015 #1
    1. The problem statement, all variables and given/known data
    A sound source is placed at the top of a tall (h = 189.6m) radio tower. The source has a frequency of 740 Hz and an amplitude of 19.4 nm at point A. The air surrounding the tower has a density of 1.29 kgm-3 and sound travels through it with a velocity of 343 ms-1. Point A is 13.5 m above the source. You may ignore any reflections of the sound from the ground.
    Calculate the average power leaving the source.

    2. Relevant equations
    P = (1/2)pAv(ws)^2
    where p = density of air = 1.29
    v = sound velocity = 343
    s = maximum displacement (amplitude) = 19.4e-9
    w = 2Pi*f = 2960*Pi
    A = area of speaker

    3. The attempt at a solution
    It seems that this question is unsolvable without being supplied with the area of the speaker. Unless the amplitude at Point A somehow depends upon this area, however I'm sure that it depends solely upon the size of the speakers vibrations, not the area of the surface causing them.
    Any help would be greatly appreciated.
     
  2. jcsd
  3. Jun 7, 2015 #2

    vela

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    The intensity of a sound wave is given in units of power per area, so starting from your expression, you'd get
    $$I = \frac PA = \frac 12 \rho v (\omega s)^2.$$ You're probably supposed to assume the speaker can be treated as a point source. How does the sound propagate away from the speaker and how does the intensity of sound vary with distance?
     
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