Question

The sound from a trumpet radiates uniformly in all directions in 20C air. At a distance of 5.00 m from the trumpet the sound intensity level is 52.0 dB. The frequency is 587 Hz. (a) What is the pressure amplitude at this distance

Answer 1

The answer is below

Step-by-step explanation:

The intensity level (B) of a sound wave is given by:

B = 10log(I/I₀);

where I₀ is the threshold intensity = 1 * 10⁻¹² W/m², I is the intensity at distance 5 m, B is the intensity level = 52 dB

Substituting gives:

`52=10log((I)/(10^(-12)) )\\\\log((I)/(10^(-12)) )=5.2\\\\I=1.58*10^(-7)\ W/m^2`

The pressure is given by:

`I=(p_(max)^2)/(2\rho v) \\\\\rho=air\ density=1.2\ kg/m^3,v=speed\ of\ sound\ in\ air=344\ m/s,p_(max)=pressure:\\\\p_(max)=√(2\rho vI)=\sqrt{2*1.58*10^(-7)*1.2*344} =1.14*10^(-2)Pa`