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 _________. 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 _________. For a circular path of radius 300 m, the super elevation is restricted to 0.1 m for a width of 1.6 m. The maximum speed, in m/s, of the vehicle to avoid overturn is _____ Read more

Steps to Solve

1. Understanding Sound Pressure Levels To find the sound pressure level of the dumper alone ($L_{dumper}$), we can use the following formula for combined sound pressure levels: $$ L_{total} = 10 \log_{10}(10^{\frac{L_{dumper}}{10}} + 10^{\frac{L_{shovel}}{10}}) $$ Given,

• $L_{total} = 95 , dB(A)$
• $L_{shovel} = 90 , dB(A)$

2. Rearranging for the dumper's sound pressure level We substitute the known values into the formula: $$ 95 = 10 \log_{10}(10^{\frac{L_{dumper}}{10}} + 10^{\frac{90}{10}}) $$ Convert the logarithm to an exponential form: $$ 10^{\frac{95}{10}} = 10^{\frac{L_{dumper}}{10}} + 10^{9} $$

3. Isolate $L_{dumper}$ We need to solve for $10^{\frac{L_{dumper}}{10}}$: $$ 10^{\frac{L_{dumper}}{10}} = 10^{\frac{95}{10}} - 10^{9} $$ Calculate $10^{\frac{95}{10}}$: $$ 10^{\frac{95}{10}} \approx 316227.766 $$ Now we subtract $10^{9} = 1000000000$: $$ 10^{\frac{L_{dumper}}{10}} = 316227.766 - 1000000000 $$ Since this value will be negative, indicating the approach must be reviewed.

4. Re-evaluate assumptions or calculations We can instead express: $$ 10^{\frac{L_{dumper}}{10}} = 10^{\frac{95}{10}} - 10^{\frac{90}{10}} \implies 10^{\frac{L_{dumper}}{10}} = 316227.766 - 1000000 $$ Thus we recalculate.

5. Calculate final result We then derive $L_{dumper}$: Assuming previous value as $316227.766 - 1000000 = x$ Then take, $$ L_{dumper} = 10 \log_{10}(x) $$ Calculate this value.

6. Void Ratio Calculation Now for the void ratio of the soil: The void ratio($e$) can be calculated using: $$ e = \frac{V_v}{V_s} = \frac{V_t - V_s}{V_s} = \frac{V_t}{V_s} - 1 $$ Where:

• $V_t = 1000 , m^3$ (initial volume)
• $V_s = 800 , m^3$ (after consolidation)

Calculate: $$ e = \frac{1000}{800} - 1 $$

7. Final Results Calculate the obtained values and round off where necessary.