Answer
The displacement amplitude, A, increases by a factor of a million between the threshold of hearing and the threshold of pain.
Work Step by Step
Equation 11–18 relates intensity I and the displacement amplitude A.
$$I=2\pi^2\rho v f^2A^2$$
Let “1” denote the threshold of hearing, and “2” denote the threshold of pain.
$$\frac{I_2}{I_1}=10^{12}=\frac{A_2^2}{A_1^2}$$
$$10^{6}=\frac{A_2}{A_1}$$
The displacement amplitude, A, increases by a factor of a million between the threshold of hearing and the threshold of pain.
