= Solution
By the <Fourier modulation and translation identity>, delaying the pulse by $\tau$ multiplies its transform by $e^{-i\omega\tau}$. Hence
$$
\boxed{\widetilde r(\omega)=(1+\alpha e^{-i\omega\tau})\widetilde b(\omega)=(1+\alpha e^{-i\omega\tau})\frac{4\sin\omega(1-\cos\omega)}{\omega^3}.}
$$
The removable value at zero is $2(1+\alpha)$. For real $\alpha$, the squared spectral magnitude is multiplied by $1+\alpha^2+2\alpha\cos(\omega\tau)$, showing the interference between the direct and reflected signals.
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