The loudest sound in Earth’s history is believed to be the explosion of the volcanic island of Krakatoa, back in 1883. Physicists estimate that the intensity of the sound produced was 1.0×107 W/m2. How many decibels does this correspond to?
Standard reference sound intensity
I₀= 10⁻¹² W/m²
I₁=10⁷W/m²
L=10 log₁₀ (I₁/I₀) =
=10 log₁₀(10⁷/10⁻¹²) =
=190 dB
To determine the number of decibels (dB) corresponding to a sound intensity of 1.0×10^7 W/m^2, we can use the formula:
dB = 10 * log10(I/I0)
Where:
- dB is the decibel level
- I is the sound intensity in watts per square meter (W/m^2)
- I0 is the reference sound intensity (typically 10^-12 W/m^2)
Using the given intensity of 1.0×10^7 W/m^2, we can calculate the decibel level as follows:
dB = 10 * log10(1.0×10^7 / 10^-12)
Converting the given intensity to scientific notation:
dB = 10 * log10(1.0 × 10^7 / 1.0 × 10^-12)
Simplifying the logarithmic calculation:
dB = 10 * log10(1.0 × 10^19)
Now, calculating the logarithm:
dB = 10 * 19
dB = 190
Therefore, the explosion of Krakatoa corresponds to approximately 190 decibels (dB).
To determine the number of decibels (dB) corresponding to a given sound intensity, you can use the formula:
dB = 10 * log10(I/I0)
Where:
- dB is the sound level in decibels,
- I is the sound intensity,
- I0 is the reference intensity, generally considered to be the threshold of human hearing, which is approximately 1.0 × 10^−12 W/m^2.
In this case, the sound intensity (I) during the explosion of Krakatoa is given as 1.0×10^7 W/m^2.
Now, let's substitute these values into the formula to find the corresponding sound level in decibels:
dB = 10 * log10(1.0×10^7 / 1.0×10^−12)
First, divide the numerator and denominator by 1.0 × 10^−12:
dB = 10 * log10(1.0×10^19)
Then, take the logarithm (base 10) of the result:
dB = 10 * 19
Finally, multiply 10 by 19 to get the sound level in decibels:
dB = 190
Therefore, the explosion of Krakatoa corresponds to a sound level of approximately 190 decibels.