Question

A very loud train whistle has an acoustic power output of 100 W. If the sound energy spreads out spherically, what is the intensity level in dB at a distance of 100 meters from the train?

Answer 1

Answer

given,

Power output of loud train = 100 W

Distance of intensity level from train= 100 m

I₀ = 10⁻¹² W/m²                      

Intensity of sound = ?        

we know,                            

$I = \dfrac{P}{Area}$          

$I = \dfrac{P}{4\pi r^2}$          

$I = \dfrac{100}{4\pi 100^2}$          

$I =7.957\times 10^{-4}\ W/m^2$

Intensity level                              

  = $10 log(\dfrac{I}{I_0})$

  = $10 log(\dfrac{7.975\times 10^{-4}}{10^{-12}})$

  = $10 \times 8.900$

  = 89 dB