A music is played causing 82 dB. A baby cries causing 72 dB annoying the people around him by 123.7 m. What is the sound intensity level?
To calculate the sound intensity level, we need to convert the decibel (dB) measurements into the corresponding sound intensity (I) values.
The formula for sound intensity level (L) in decibels is given by:
L = 10 * log10(I/I0)
Where:
L is the sound intensity level in decibels,
I is the sound intensity in watts per square meter (W/m^2), and
I0 is the reference sound intensity equal to 10^(-12) W/m^2.
First, let's calculate the sound intensity (I) for the music that produced 82 dB:
I_music = I0 * 10^(L_music/10)
= (10^(-12) W/m^2) * 10^(82/10)
= (10^(-12) W/m^2) * 10^8.2
Similarly, let's calculate the sound intensity (I) for the baby's cry that caused 72 dB:
I_baby = I0 * 10^(L_baby/10)
= (10^(-12) W/m^2) * 10^(72/10)
= (10^(-12) W/m^2) * 10^7.2
Now, we can find the sound intensity level (L_annoyance) caused by the baby's cry annoyance to people around:
L_annoyance = L_music - L_baby
= 10 * log10(I_music/I0) - 10 * log10(I_baby/I0)
= 10 * (log10(I_music) - log10(I_baby))
Finally, substitute the calculated sound intensities into the formula to find the sound intensity level:
L_annoyance = 10 * (log10[(10^(-12) W/m^2) * 10^8.2] - log10[(10^(-12) W/m^2) * 10^7.2])
By evaluating this expression, you will get the sound intensity level caused by the baby's cry annoyance to people nearby.