We know $$P = F\cdot v$$ where $v$ is the velocity vector. Since at the "displacement nodes" in a standing sound wave the velocity of the particles is always 0, the Power must be 0 and hence the Intensity of sound wave at these positions must also be 0 as $$I =\frac{P}{A}$$
where $A$ is area. But sound intensity is maximum at these points. Can someone explain this to me, please.
Best Answer
The easiest way is to join both the formulas in definition of sound intensity:
$$ i = pv $$
where $p$ and $v$ are acoustical pressure and velocity respectively. In a standing wave there is a $\pi/2$ phase shift between them and hence the intensity maxima out the nodes and antinodes of pressure and velocity.
However, usually you use and measure not the immediate intensity $i$, but it's mean value in time $I$ which is:
$$ I = \frac{p^2_{acoustic \ RMS}}{\rho_0 c_0} $$