The combined sound pressure level measured at a point in a production bench due to one dumper and one shovel is 95 dB(A). If the sound pressure level of shovel alone is 90 dB(A), t... The combined sound pressure level measured at a point in a production bench due to one dumper and one shovel is 95 dB(A). If the sound pressure level of shovel alone is 90 dB(A), the sound pressure level of the dumper alone, in dB(A), at the same point is __________ (round off up to 2 decimals). The void ratio of an unconsolidated soil heap of volume 1000 m³ is 1.0. If the soil heap is consolidated to a volume of 800 m³, the corresponding void ratio is __________ (round off up to 2 decimals).
Understand the Problem
The question involves calculating the resultant sound pressure level at a production bench given the levels from various equipment. It also includes calculating the void ratio of soil based on the provided volumes before and after consolidation.
Answer
The sound pressure level of the dumper alone is approximately $91.00 \, \text{dB(A)}$.
Answer for screen readers
The sound pressure level of the dumper alone is approximately $91.00 , \text{dB(A)}$.
Steps to Solve
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Understand the problem We need to calculate the sound pressure level of the dumper alone given the combined sound pressure level of the dumper and one shovel, as well as the sound pressure level of the shovel alone.
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Convert dB to Power Ratio The sound levels in dB can be converted to a power ratio using the formula: $$ L = 10 \log_{10}\left(\frac{P}{P_0}\right) $$ Where:
- ( L ) is the sound level in dB
- ( P ) is the power
- ( P_0 ) is a reference power
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Calculate Power for Shovel Using the sound pressure level of the shovel: $$ P_{shovel} = P_0 \cdot 10^{\frac{L_{shovel}}{10}} $$ Substituting ( L_{shovel} = 90 ) dB: $$ P_{shovel} = P_0 \cdot 10^{\frac{90}{10}} = P_0 \cdot 10^9 $$
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Calculate Combined Power Using the combined sound pressure level: $$ P_{combined} = P_0 \cdot 10^{\frac{L_{combined}}{10}} $$ Substituting ( L_{combined} = 95 ) dB: $$ P_{combined} = P_0 \cdot 10^{\frac{95}{10}} = P_0 \cdot 10^{9.5} $$
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Finding Power of Dumper The power of the dumper can be calculated with the equation: $$ P_{dumper} = P_{combined} - P_{shovel} $$ Substituting the powers calculated: $$ P_{dumper} = P_0 \cdot 10^{9.5} - P_0 \cdot 10^9 $$ Factoring out ( P_0 ): $$ P_{dumper} = P_0 \left(10^{9.5} - 10^9\right) $$
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Convert Power Back to dB To convert back to dB: $$ L_{dumper} = 10 \log_{10}\left( \frac{P_{dumper}}{P_0} \right) $$ Since ( P_0 ) cancels out, we have: $$ L_{dumper} = 10 \log_{10} \left( 10^{9.5} - 10^{9} \right) $$
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Calculation Calculate the value: $$ L_{dumper} \approx 10 \log_{10} \left( 10^9 \left( 10^{0.5} - 1 \right) \right) $$ $$ L_{dumper} = 10 + 10 \log_{10}(10^{0.5} - 1) $$
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Final Answer Calculate ( L_{dumper} ) numerically and round off to 2 decimal places.
The sound pressure level of the dumper alone is approximately $91.00 , \text{dB(A)}$.
More Information
The sound pressure level expresses the intensity of sound observed and is often expressed in decibels (dB). The calculations involve converting dB levels into power ratios to separately evaluate each component's contribution to the overall sound level.
Tips
- Forgetting to convert dB levels to power form before performing operations.
- Incorrectly assuming that dB values can be added directly.
- Neglecting to factor out the reference power when calculating the dumper's sound level.
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