A very loud train whistle has an acoustic power output of 94 W.If the sound energy spreads out spherically,what is the intensity level in dB at a distance of 95 meters from the train? (I₀ = 10−¹² W/m²)

Question

Quizplus · Accepted Answer

The formula relating power and intensity is:
P = I*A
where P is power, I is intensity, and A is the area through which the sound is passing. Since the sound energy spreads out spherically, the area through which it is passing increases as distance from the source increases. Specifically, the area of a sphere is given by:
A = 4*pi*r^2
where r is the distance from the source. 
Combining these two equations, we can solve for intensity:
I = P/(4*pi*r^2)
Plugging in the given values, we get:
I = 94/(4*pi*95^2) = 1.28 x 10^-5 W/m^2
Next, we use the formula for sound level in decibels:
L = 10*log(I/I0)
where I0 is the reference intensity, which is defined as:
I0 = 10^-12 W/m^2
Plugging in the values, we get:
L = 10*log(1.28 x 10^-5/10^-12) = 89 dB.

A Very Loud Train Whistle Has an Acoustic Power Output