Two people hear a tornado siren, but one listener is 49.5 times farther away from the source of the sound than the other. What is the intensity level of the sound (in decibels) for the farther listener relative to the other listener?

B = - 33.89 dB

Explanation: The intensity of sound wave and square of distance from the source have an inverse relationship. This is given below as

Io/(r1)² = I/(r2)²

Where Io = intensity at a distance r1 away from source and I = intensity at a distance r2 away from the source.

For simplicity, we let our r1 = r in this question.

From the question, the farther listener is 49.5 times the distance of the closer listener away from the source.

That's if r1 =r then r2 = 49.5 ×r2.

By slotting this into the relationship above we have that

Io/r² = I/(49.5 ×r²)

Io/r² = I/(49.5)² × r².

We have that

Io×r² = I ×(49.5)² ×r²

r² cancels out on both sides of equation, we have that

Io = I(49.5)²

I/Io = I/(49.5)²

The sound intensity level is given as

B = 10 log ( I/Io)

But I/Io = I/(49.5)²

B = 10 log ( 1/(49.5)²)

B = 10 log ( 1/2450.25)

B = 10 × (-3.389)

B = - 33.89 dB

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y