The drilling of a jackhammer was measured at 131dB. The sound of whispering was measured at 28dB. (Note that log2=0.301). The ratio of the intensity of the drilling to that of the whispering would be approximately:
10^((131-28)/10) = 10^10.3
To find the ratio of the intensity of the drilling to that of the whispering, we need to calculate the difference in decibels (dB) between the two sound levels.
The formula to calculate the difference in dB is:
Difference in dB = 10 * log10(I1/I2)
Where I1 is the intensity of sound source 1 and I2 is the intensity of sound source 2.
First, let's convert the given dB values to intensity levels using the formula:
I = 10^(dB/10)
For the drilling sound:
I_drilling = 10^(131/10) = 1995262.314
I_whispering = 10^(28/10) = 0.001584893
Now, let's calculate the difference in dB using the formula:
Difference in dB = 10 * log10(I1/I2)
= 10 * log10(I_drilling/I_whispering)
= 10 * log10(1995262.314/0.001584893)
Using a calculator, the difference in dB is approximately 43.962.
Since we want to find the ratio of the intensity, we need to convert the difference in dB back to a ratio using the formula:
Ratio = 10^(dB/10)
Ratio = 10^(43.962/10)
Using a calculator, the ratio of the intensity of the drilling to the whispering sound is approximately 294797.788.
To find the ratio of the intensity of the drilling to that of the whispering, we need to calculate the difference in decibels (dB) between the two measurements and then convert it to intensity ratio.
The formula to convert decibels to intensity ratio is:
Intensity Ratio = 10^((dB1 - dB2) / 10)
Here, dB1 is the measurement of the drilling (131dB) and dB2 is the measurement of the whispering (28dB).
So, let's calculate the intensity ratio:
Difference in decibels = 131dB - 28dB = 103dB
Intensity Ratio = 10^(103 / 10) ≈ 10^10.3
Using the approximate value of log2 (0.301), we can rewrite it as:
Intensity Ratio ≈ 10^(10.3 * log2) ≈ 10^(3.113)
Therefore, the ratio of the intensity of the drilling to that of the whispering would be approximately 10^3.113.