Question

Average noise level at a working place is 80 dB(A) for the first 10 minutes and 60 dB(A) for the next 30 minutes. The energy equivalent continuous noise level at the place for the entire period of 40 minutes, in dB(A), is:

Hint:

Use the energy-based average (Leq) to accurately calculate varying noise exposure over time. Always convert dB values using base-10 exponentials before averaging.

Answer 1

Step 1: Use the formula for equivalent continuous noise level \( L_{eq} \):
\[ L_{eq} = 10 \log_{10} \left( \frac{1}{T} \sum_{i=1}^{n} t_i \cdot 10^{L_i/10} \right) \]

\[ L_{eq} = 10 \log_{10} \left( \frac{1}{40} (10 \cdot 10^8 + 30 \cdot 10^6) \right) = 10 \log_{10} \left( \frac{10^9 + 9 \cdot 10^7}{40} \right) \]
\[ = 10 \log_{10} \left( \frac{1090000000}{40} \right) \]
\[ 10 \log_{10} (27250000) \]
\[ \approx 10 \times \log_{10}(2.725 \times 10^7) \]
\[ = 10 \left( \log_{10}(2.725) + 7 \right) \]
\[ = 10 (0.435 + 7) \]
\[ = 10 \times 7.435 \]
\[ = \boxed{73.35 \approx 73} \]