What is pressure amplitude and when is it the maximum?

Question

i started learning about sound waves and i came across compression waves

soo the final equation u get is

$$\Delta P =\Delta P_o*\cos(wt-kx)$$ $$\Delta P_o=B*K*A$$

here $$\Delta P_o$$ is the pressure amplitude

B and A are the bulk modulus and Amplitude of the wave

Now, what is pressure amplitude ?? I did find some internet results and apparently, it is the maximum difference in pressure but I don't understand how it is related to the pressure difference .:( [can some please elaborate on this info]

https://physics.info/intensity/#:~:text=The%20pressure%20amplitude%20is%20the,the%20maximum%20change%20in%20density. [the link,line 11]

also, when is it maximum??

Answer 1

For any wave of the form$$y=A\,sin(x)$$ A is called the amplitude

Amplitude by definition is the maximum extent of a vibration or oscillation, measured from the position of equilibrium

This is same as the value of maximum fluctuation in pressure, here that is between $0$ (when $cos(...)=0$) to $\Delta{P}_0$ (when $cos(...)=1$)

In the very same sense the coefficient of the $cos(...)$ have which is $\Delta{P}_0$ is called the Amplitude. Amplitude is maximum when the $cos$ factor is $1$, which happens when the argument that is $\omega{t}-kx=2n\pi$