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Elastic Waves. Acoustics.

Problem 4.158

Find the radius vector defining the position of a point source of spherical waves if that source is known to be located on the straight line between the points with radius vectors \(\mathbf{r}_ {1}\) and \(\mathbf{r}_ {2}\) at which the oscillation amplitudes of particles of the medium are equal to \(a_{1}\) and \(a_{2}\). The damping of the wave is negligible, the medium is homogeneous.

Reveal Answer
r=(a1r1+a2r2)/(a1+a2)\mathbf{r}=\left(a_{1} \mathbf{r}_{1}+a_{2} \mathbf{r}_{2}\right) /\left(a_{1}+a_{2}\right)
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