Explanation

(d) Given,
$y = 5\sin\left( 30\pi t - \frac{\pi}{7}x + 30{^\circ} \right)\ldots(i)$
Now,
$y = a\sin\left( \frac{2\pi t}{T} - \frac{2\pi x}{\lambda} + \phi \right)\ \ \ \ldots(ii)$
On comparing Eqs. (i) and (ii)
$\frac{2\pi x}{\lambda} = \frac{\pi x}{7}$
$\Longrightarrow \ \ \ \ \lambda = 14m$
We know that relation between phase difference and path difference
$\mathrm{\Delta}\phi = \frac{2\pi}{\lambda} \times \mathrm{\Delta}x = \frac{2\pi}{14} \times 3.5$
$\Longrightarrow \mathrm{\Delta}\phi = \frac{\pi}{2}$