Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2.
F
decibels=10Log(base 10)(P1/P0),
where P0 is the threshold of hearing, or 10^-12 W/M^2
To calculate the sound level in decibels (dB) of a sound wave, you can use the equation:
L = 10 * log10(I / I₀)
where L is the sound level in decibels, I is the intensity of the sound wave, and I₀ is the reference intensity.
In this case, the intensity of the sound wave is given as 2.25 µW/m^2.
To find the reference intensity, we need to understand that 0 decibels (dB) corresponds to the reference intensity. The reference intensity for sound is commonly defined as 1 picowatt per square meter (1 pW/m^2).
Now, let's substitute the given values into the equation:
L = 10 * log10(2.25 µW/m^2 / 1 pW/m^2)
To simplify the calculation, it is necessary to convert both the numerator and denominator to the same units. In this case, we will convert 2.25 µW to picowatts:
L = 10 * log10(2.25 µW/m^2 / 1 pW/m^2)
= 10 * log10(2.25 / 10^-6)
Using logarithmic properties, log10(2.25 / 10^-6) can be simplified:
L = 10 * log10(2.25 * 10^6)
= 10 * log10(2.25) + 10 * log10(10^6)
= 10 * log10(2.25) + 10 * 6
= 10 * (log10(2.25) + 6)
Evaluating log10(2.25) using a calculator, we find that it is approximately 0.352.
L = 10 * (0.352 + 6)
= 10 * 6.352
= 63.52 dB
Therefore, the sound level in decibels of a sound wave with an intensity of 2.25 µW/m^2 is approximately 63.52 dB.