The intensity of a sound wave is given by the formula:
I = P/A
Where: I is the intensity of the sound wave P is the power carried by the sound wave A is the area through which the sound wave is propagating
In this case, the given information provides the intensity level, which is expressed in decibels (dB). The intensity level (IL) is related to the intensity (I) by the formula:
IL = 10 * log10(I/I₀)
Where: IL is the intensity level in decibels I₀ is the reference intensity (threshold of hearing) which is approximately 1 x 10^(-12) W/m^2
To find the intensity (I) from the intensity level (IL), we rearrange the formula:
I = I₀ * 10^(IL/10)
Given: IL = 80 dB
Substituting the values into the formula:
I = (1 x 10^(-12)) * 10^(80/10) I = (1 x 10^(-12)) * 10^8 I = 1 x 10^(-12+8) I = 1 x 10^(-4) W/m^2
Therefore, the intensity of the sound wave is 1 x 10^(-4) W/m^2.