Calculating Sound Level of a Firecracker Explosion

If two firecrackers produce a combined sound level of 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded?

Understanding Sound Level Calculation

Sound Level Calculation: The sound level in decibels (dB) is a logarithmic scale that measures the intensity of sound relative to a reference level. When two sound sources are combined, their intensities are summed, not their dB values. To calculate the combined sound level when two firecrackers are fired simultaneously, we can use the following formula: L_combined = 10 * log10(I1 + I2) where L_combined is the combined sound level in dB, I1 and I2 are the intensities of the two firecrackers. Given that the combined sound level is 85 dB, we can rearrange the formula to solve for the combined intensity (I1 + I2): I1 + I2 = 10^(L_combined / 10) Now, to find the sound level when only one firecracker is exploded, we can use the formula: L_single = 10 * log10(I_single) where L_single is the sound level in dB when one firecracker is exploded, and I_single is the intensity of the single firecracker. Since the intensity of the single firecracker is half of the combined intensity (assuming the firecrackers have equal intensities), we can substitute I_single = (I1 + I2) / 2 into the formula to calculate L_single: L_single = 10 * log10((I1 + I2) / 2) Substituting the calculated value of I1 + I2 from the earlier step, we can find the sound level when only one firecracker is exploded. Therefore, if two firecrackers produce a combined sound level of 85 dB when fired simultaneously, the sound level when only one firecracker is exploded will be approximately 82 dB. This calculation is based on the assumption that the firecrackers have equal intensities.
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