What sound intensity level in dB is produced by earphones that create an intensity of 4.00¡¿10^-2 W/m^2?

To find the sound intensity level in decibels (dB) produced by the earphones, you can use the formula:

dB = 10 * log10(I/I₀)

Where:
- dB is the sound intensity level in decibels,
- I is the sound intensity in watts per square meter (W/m^2),
- I₀ is the reference sound intensity which is 1.00 x 10^(-12) W/m^2.

In this case, the given sound intensity is I = 4.00 x 10^(-2) W/m^2.

Plugging in the values into the formula:

dB = 10 * log10(4.00 x 10^(-2)/1.00 x 10^(-12))

To simplify the calculation, divide the numerator and denominator by 1.00 x 10^(-12):

dB = 10 * log10(4.00 x 10^(-2)/1.00 x 10^(-12)) = 10 * log10(4.00 x 10^(10))

Now, calculate the value within the logarithm:

4.00 x 10^(10) = 4.00 x 10^(1) x 10^(10) = 4.00 x 10^(11)

Take the logarithm of 4.00 x 10^(11) with base 10:

log10(4.00 x 10^(11)) = 11

Plug this value back into the original formula:

dB = 10 * 11 = 110 dB

Therefore, the sound intensity level produced by the earphones is 110 dB.