= Solution
The <Strong Huygens principle> in three spatial dimensions says that the solution at $(t,x)$ depends only on the initial data on the sphere
$$
\{y:|y-x|=|t|\},
$$
rather than on the full ball bounded by that sphere. This follows immediately from the Kirchhoff formula and its time derivative. Consequently a disturbance has no tail inside the light cone: if the initial data are supported in a compact set $K$, then $u(t,x)=0$ whenever that sphere misses $K$. This is sharper than <finite propagation speed>, which only excludes influence from outside the ball.
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