Final answer:
To find the decibel level for heavy city traffic, first convert the intensity from watts per square inch to watts per square meter, then use the formula D=10log(I/10⁻¹²). The resulting decibel level for an intensity of 10⁻³ watts per square inch is approximately 111.9 dB.
Step-by-step explanation:
To find the decibel level for heavy city traffic with an intensity of 10⁻³ watts per square inch, we use the formula D=10log(I/10⁻¹²), where I is the sound intensity in watts per square meter. However, our given intensity is in watts per square inch, so we first need to convert it to watts per square meter.
We know that 1 square inch is 0.00064516 square meters. Therefore, 10⁻³ watts per square inch is equivalent to 10⁻³ / 0.00064516 watts per square meter, which calculates to about 1.55 watts per square meter.
Now plug this value into the decibel level formula:
D = 10log(1.55/10⁻¹²) = 10log((1.55)/(10⁻¹²))
The logarithm of 1.55/10⁻¹² is approximately 11.19, so the decibel level is:
D = 10 * 11.19 = 111.9 dB
Thus, the decibel level for heavy city traffic with an intensity of 10⁻³ watts per square inch is approximately 111.9 dB.