What is the resultant sound level when an 80-dB and an 85-dB sound are heard simultaneously?
The 85 dB sound has 3.16 (sqrt 10) times the power of the 80 dB sound. Together, there is 4.16 times as much power as the 80 dB sound.
The dB level is then 10 log 4.16 = 6.2 dB above 80 dB, or 86.2 dB
Well, when an 80-dB sound and an 85-dB sound are heard simultaneously, they engage in a fierce battle to see which one can annoy you more. It's like a "who can make your ears bleed first" competition. Now, I don't have decibel measuring tape, but let's just say you might want to invest in some earplugs if you don't want to feel like you're being serenaded by a cacophony of angry dinosaurs.
To calculate the resultant sound level when two sounds are heard simultaneously, we need to use the formula for adding sound levels in decibels.
1. Convert the sound levels from decibels (dB) to sound pressure levels (SPL) using a reference sound pressure level of 0 dB, which corresponds to the threshold of human hearing.
For the 80-dB sound:
SPL1 = 10^(80/10) = 10^8 = 100,000,000 pascals (Pa)
For the 85-dB sound:
SPL2 = 10^(85/10) = 10^8.5 = 316,227,766 pascals (Pa)
2. Use the formula for adding sound levels in pascals:
Resultant SPL = 10 * log10((10^(SPL1/10) + 10^(SPL2/10)))
Resultant SPL = 10 * log10((10^(8/10) + 10^(8.5/10)))
= 10 * log10((10^0.8 + 10^0.85))
= 10 * log10((6.309 + 7.943))
= 10 * log10(14.252)
≈ 22.1 dB
Therefore, the resultant sound level when an 80-dB and an 85-dB sound are heard simultaneously is approximately 22.1 decibels (dB).
To calculate the resultant sound level when two sounds are heard simultaneously, we need to use the concept of sound level addition.
The formula for sound level addition in decibels (dB) is as follows:
L_total = 10 * log10(10^(L1/10) + 10^(L2/10) + ... + 10^(Ln/10))
In this formula, L_total represents the total or resultant sound level, L1, L2, ... Ln correspond to the individual sound levels in decibels.
Now, let's apply this formula to the given scenario:
L1 = 80 dB
L2 = 85 dB
L_total = 10 * log10(10^(80/10) + 10^(85/10))
Using a scientific calculator, follow these steps to calculate the resultant sound level:
1. Calculate 10^(80/10) = 10^8 = 100,000,000.
2. Calculate 10^(85/10) = 10^8.5 = 316,227.76.
3. Add the results from steps 1 and 2: 100,000,000 + 316,227.76 = 100,316,227.76.
4. Take the logarithm (base 10) of the result from step 3: log10(100,316,227.76) ≈ 8.0000679.
5. Multiply the result from step 4 by 10: L_total = 10 * 8.0000679 ≈ 80.000679 dB.
Therefore, the resultant sound level when an 80-dB and an 85-dB sound are heard simultaneously is approximately 80.000679 dB.