Question

Your bedroom is 8.0 m away from the living room. When requested by your parents to turn down your stereo, you do, and the intensity level where they are sitting in the living room drops from 54 dB to 45 dB.

What is the change in the power of the sound emitted by your stereo?

Express your answer with the appropriate units.

P45dB−P54dB=

Answer 1

Given that Sound intensity level is

SLf = Sound level final = 45 dB

SLi = Sound level initial = 54 dB

Sound level is given by:

SL = 10*log (I/I0)

I0 = threshold level = 10^-12 W/m^2

So,

SLf = 45 = 10*log(If/I0)

If = I0*(10^4.5)

Similarly,

SLi = 54 = 10*log(Ii/I0)

If = I0*(10^5.4)

For a constant power source,

Power = Intensity*Area

I = P/A

P = I*A

So, the change in the power of the sound emitted by your stereo will be,

Pi - Pf = A*(Ii - If)

here, A = 4*pi*r^2

given, r = 8.0 m

So, Pi - Pf = (4*pi*8^2)*I0*(10^5.4 - 10^4.5)

Pi - Pf = (4*pi*8^2)*(10^-12)*(10^5.4 - 10^4.5)

Pi - Pf = 1.76*10^-4 W

Pi - Pf = 0.176 mW

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