Two identical machines are positioned the same distance from a worker. The intensity of sound delivered by each machine at the location of the worker is $2.0 \times 10^{-7} W / m ^{2}$ . Find the sound level heard by the worker

(A) when one machine is operating

(B) when both machines are operating.

Question

Two identical machines are positioned the same distance from a worker. The intensity of sound delivered by each machine at the location of the worker is $2.0 \times 10^{-7} W / m ^{2}$ . Find the sound level heard by the worker

(A) when one machine is operating

(B) when both machines are operating.

(A) when one machine is operating

(B) when both machines are operating.

Accepted Answer

(A) The sound level at the location of the worker with one machine operating is calculated from Equation 17.8:

[latex] \beta \equiv 10 \log \left(\frac{I}{I_{0}} ight) [/latex] (17.8).

[latex] \beta_{1}=10 \log \left(\frac{2.0 imes 10^{-7} W / m ^{2}}{1.00 imes 10^{-12} W / m ^{2}} ight)=10 \log \left(2.0 imes 10^{5} ight) [/latex].

[latex] =53 dB [/latex].

(B) When both machines are operating, the intensity is doubled to [latex] 4.0 imes 10^{-7} W / m ^{2} ext {; therefore, the sound level now is } [/latex]

[latex] \beta_{2}=10 \log \left(\frac{4.0 imes 10^{-7} W / m ^{2}}{1.00 imes 10^{-12} W / m ^{2}} ight)=10 \log \left(4.0 imes 10^{5} ight) [/latex].

[latex] =56 dB [/latex].

From these results, we see that when the intensity is doubled, the sound level increases by only 3 dB.

Question 17.4: Two identical machines are positioned the same distance from...

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