Starting with Eq. (4.1-10), show that if \(\Delta v \ll \bar{v}\) and \(r \ll 2 c / \Delta v\) for all \(P_{1}\), then

\[ \mathbf{u}\left(P_{0}, t\right) \approx \iint_{\Sigma} \frac{e^{j 2 \pi(r / \bar{\lambda})}}{j \bar{\lambda} r} \mathbf{u}\left(P_{1}, t\right) \chi(\theta) d S \]

can be used to describe the propagation of \(\mathbf{u}(P, t)\). Here \(\bar{\lambda}=c / \bar{v}\).