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Sound intensity and relationship to pressure and displacement

  1. Jan 4, 2013 #1
    1. The problem statement, all variables and given/known data

    The sound from a trumpet radiates uniformly in all directions in air with a temperature of 20 degC. At a distance of 4.80m from the trumpet, the sound intensity level is 47.0dB. The frequency is 576Hz. Also knowing speed of sound in air is 344m/s, the density is 1.20kg/m^3 and the reference intensity is 10^-12 W/m^2, what is the pressure amplitude at this distance?

    2. Relevant equations

    I'm not given anything but from memory I know I = [itex]\frac{1}{2}[/itex] Bk[itex]\omega[/itex]A^2 or I = [itex]\frac{1}{2}[/itex] [itex]\sqrt{}(\rho B\omega ^2 A^2)[/itex]

    Also: sound level = 10log[itex]_{10}[/itex]([itex]\frac{I}{I_{0}}[/itex])

    3. The attempt at a solution

    I've got three chances at an answer on the system I use and have spent the first two calculating I to be 10^-7.3 and using I = Pressure x velocity to give Pmax = 1.46*10^-10. Wrong. Then I used the reference pressure (I looked up on the trustworthy internet) and the slight variation of the sound level formula to give Pmax = 4.48*10^-3. Also wrong.

    (I have since realised where I used velocity above, it's probably velocity of medium and not of sound in medium)

    The question after asked for the displacement amplitude (now being given the Bulk modulus as 1.42*10^5 Pa). Using the formula I gave above for intensity in terms of B, rho and omega etc, I calculated that this should be 6.71*10^-14m. Surprise, surprise: wrong again.


    Many, many thanks in advance
     
  2. jcsd
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