Question: 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},
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 \(\bar{\lambda}=c / \bar{v}\).
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To demonstrate that the given integral equation can describe the propagation of mathbfuP t under the specified conditions we need to start with the eq... View full answer
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