To find the phase difference between two layers of the wave, we first need to identify the wave number from the given equation and then use the formula for phase difference. Step 1: Identify the wave number ($k$) from the given wave equation. The general equation for a progressive wave is given by: $$y = A\text{Sin}(\omega t - kx)$$ The given equation is: $$y = 10\text{Sin}\left(1000\pi t - \frac{\pi x}{34}\right)$$ By comparing the two equations, we can see that the wave number $k$ is: $$k = \frac{\pi}{34} \text{ rad/cm}$$ Step 2: Calculate the phase difference ($\Delta \phi$). The phase difference $\Delta \phi$ between two points separated by a distance $\Delta x$ is given by the formula: $$\Delta \phi = k \Delta x$$ We are given the separation distance $\Delta x = 153 \text{ cm}$. Substitute the values of $k$ and $\Delta x$ into the formula: $$\Delta \phi = \left(\frac{\pi}{34} \text{ rad/cm}\right) \times (153 \text{ cm})$$ $$\Delta \phi = \frac{153\pi}{34} \text{ radians}$$ Step 3: Convert the phase difference from radians to degrees. We know that $\pi \text{ radians} = 180^\circ$. So, to convert $\Delta \phi$ to degrees, we multiply by $\frac{180^\circ}{\pi \text{ radians}}$: $$\Delta \phi = \frac{153\pi}{34} \times \frac{180^\circ}{\pi}$$ $$\Delta \phi = \frac{153 \times 180^\circ}{34}$$ Now, perform the multiplication and division: $$\Delta \phi = \frac{27540^\circ}{34}$$ $$\Delta \phi = 810^\circ$$ Step 4: Find the equivalent phase difference within $0^\circ$ to $360^\circ$. A phase difference of $810^\circ$ means the wave has completed multiple cycles. To find the equivalent angle within a single cycle ($0^\circ$ to $360^\circ$), we subtract multiples of $360^\circ$: $$810^\circ = 2 \times 360^\circ + 90^\circ$$ So, the phase difference is equivalent to $90^\circ$. Comparing this result with the given options: A. $270^\circ$ B. $45^\circ$ C. $90^\circ$ D. $180^\circ$ E. No Correct Option The calculated equivalent phase difference matches option C. The final answer is $\boxed{\text{C. } 90^0}$.