Final answer:
The sound level heard by the worker when one machine is operating is approximately 80 dB. The sound level heard by the worker when two machines are operating is approximately 86 dB.
Step-by-step explanation:
To find the sound level heard by the worker when one machine is operating, we can use the formula:
Sound level (dB) = 10 * log10(I/Io)
where I is the sound intensity in watts per meter squared and Io is the reference intensity.
Given that the intensity of sound delivered by each operating machine at the worker's location is 2 × 10^-7 W/m² and Io = 1 × 10^-12 W/m², we can substitute these values into the formula to calculate the sound level: Sound level (dB) = 10 * log10(2 × 10^-7 / 1 × 10^-12)
By evaluating the expression, we find that the sound level heard by the worker when one machine is operating is approximately 80 dB.
To find the sound level heard by the worker when two machines are operating, we need to consider the effect of the two machines on the sound intensity. Since the machines are identical and positioned the same distance from the worker, the total intensity is twice the intensity of one machine. Therefore, the total sound intensity is 2 * (2 × 10^-7) = 4 × 10^-7 W/m².
Using the same formula as before, we can calculate the sound level: Sound level (dB) = 10 * log10(4 × 10^-7 / 1 × 10^-12)
By evaluating the expression, we find that the sound level heard by the worker when two machines are operating is approximately 86 dB.