The sound intensity of 1.0 x 10^-12 J/(m^2*s) is the threshold of hearing for humans. What is the amplitude of the motion of the air molecules? Use v=340m/s and 1.2 kg/m^3 as the density of air.
I believe the formula I would use for this is I=1/2*v*p*A^2*w^2 ...but im not sure because I don't know what w is..
To find the amplitude of the motion of the air molecules, we can make use of the formula you mentioned, I = 1/2 * v * p * A^2 * w^2, where:
I = sound intensity (given as 1.0 x 10^-12 J/(m^2*s))
v = speed of sound in air (given as 340 m/s)
p = density of air (given as 1.2 kg/m^3)
A = amplitude of motion of air molecules (unknown)
w = angular frequency of the sound wave (unknown)
The formula you mentioned is actually the formula for sound intensity in terms of the amplitude of motion of the air molecules. We can rearrange the formula to solve for A:
A = sqrt(2 * I / (v * p * w^2))
Now, we need to find the value of w. The relationship between the angular frequency (w) and the frequency (f) is given by the equation w = 2 * π * f.
Since we are given the threshold of hearing (which corresponds to the lowest audible frequency for humans), we know that the corresponding frequency is 20 Hz.
Now, we can substitute the known values into the equation and solve for A:
A = sqrt(2 * (1.0 x 10^-12 J/(m^2*s)) / (340 m/s * 1.2 kg/m^3 * (2 * π * 20 Hz)^2))
Evaluating this expression will give you the amplitude of the motion of the air molecules.