# Sound intensity and relationship to pressure and displacement

1. Jan 4, 2013

### buzsh

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 = $\frac{1}{2}$ Bk$\omega$A^2 or I = $\frac{1}{2}$ $\sqrt{}(\rho B\omega ^2 A^2)$

Also: sound level = 10log$_{10}$($\frac{I}{I_{0}}$)

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.