Question

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 54 dB by an observer 10 km away. (a) What is the average power generated by the horn? W (b) What intensity level of the horn's sound is observed by someone waiting at an intersection 48 m from the train? Treat the horn as a point source and neglect any absorption of sound by the air. dB

Answer 1

sound intensity level = = 10log₁₀(I/I_o), it's unit is dB or decibel

I = intensity = power/area, it is measured in W/m²

I_o = threshold of human hearing = 10^-12W/m²

sound intensity = sound power / (4 pi R²)

sound intensity level = L_I = 10 log ( I / I₀ )

10^5.4 = power/4 pi r² * 10^-12

power = 315.65 W

b) sound intensity, I, inversely depends on square of distance

I₁/I₂ = r₂²/r₁² => I₂ = I₁*r₁²/r₂² => I₂ = kI₁, where k = r₁²/r₂² = 43402.77

= 10log(I₂/I_o) = 10log(kI₁/Io) = 10log(k/I_o) + 10log(I1/I_o) = 46.37 + 120 + 54 = 220.37 dB