I wonder is there any relationship between frequency and amplitude of wave. Generally, most of the people say that frequency and amplitude are independent to each other. But in this case, where it is a sound wave, the intensity, $I$ can be expressed in this form: $$I=\frac12\rho v\omega^2x^2$$
- $I$ is intensity of the sound wave
- $\rho$ is the density of the medium
- $v$ is the speed of sound being transmitted
- $\omega$ is the angular frequency
- $x$ is the amplitude of sound
So, judging from this formula, I suppose that the frequency should be inversely proportional to the amplitude, but why it is not like what I think? I get the formula from Halliday and Resnick physics book.