A noisy grinding machine in a factory produces a soundintensity of 1.0⋅10−5W/m2 . What is thesound level of this machine? A second identical machine is brought into the factory. Whatis the new sound intensity? What is the new sound level?

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Clara Reese · Accepted Answer

The sound level in decibles (dB) is given by the equation: beta (in dB) =10log⁡(IIo) where... beta = sound level in dB I = intensity of the sound in Wm2 I_o = intensity of a reference value* = 1.0 x 10−12Wm2 Plugging in these values we get: β(∈dB)=10log⁡(1.0x10−5Wm2/1.0x10−12Wm2)=70dB The intensity of a sound is additive. This means that ifa second machine were brought into the factory the combinedintensity of the new sound would be the sum of the individualintensities. So, &quot;I&quot; now equals: 1.0x10−5+1.0x10−5=2.0x10−5 Plugging this value back into our formula for soundlevel: beta (in dB) =10log⁡(2.0x10−5Wm2/1.0x10−12Wm2)=73dB * The Io value is a reference value and can be any value youchoose. Generally it is considered the minimum intensity ofsound that a human ear can hear, or 1.0x10−12Wm2. Hope this helps!

A noisy grinding machine in a factory produces a soundintensity of 1.0 * 10-5 W/m2 .

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