Step 1: Identify the wave number $k$ from the given wave equation. The general equation for a progressive wave is $y = A \sin(\omega t - kx)$. The given equation is $y = 10 \sin\left(1000\pi t - \frac{\pi x}{34}\right)$. By comparing the two equations, we can identify the wave number $k$: $$k = \frac{\pi}{34}$$ Step 2: Use the formula for phase difference. The phase difference $\Delta \phi$ between two points separated by a distance $\Delta x$ is given by: $$\Delta \phi = k \Delta x$$ Step 3: Substitute the given values into the formula. The distance between the two layers is $\Delta x = 153$ cm. Substitute $k = \frac{\pi}{34}$ and $\Delta x = 153$ cm: $$\Delta \phi = \frac{\pi}{34} \times 153$$ Step 4: Calculate the phase difference in radians. $$\Delta \phi = \frac{153\pi}{34}$$ To simplify the fraction, we can notice that $153 = 9 \times 17$ and $34 = 2 \times 17$. $$\Delta \phi = \frac{9 \times 17 \times \pi}{2 \times 17}$$ $$\Delta \phi = \frac{9\pi}{2} \text{ radians}$$ Step 5: Convert the phase difference from radians to degrees. We know that $\pi$ radians is equal to $180^\circ$. $$\Delta \phi = \frac{9}{2} \times 180^\circ$$ $$\Delta \phi = 9 \times 90^\circ$$ $$\Delta \phi = 810^\circ$$ Step 6: Compare the result with the given options. The calculated phase difference is $810^\circ$. The given options are: A. $270^\circ$ B. $450^\circ$ C. $900^\circ$ D. $180^\circ$ E. No Correct Option Since $810^\circ$ is not among options A, B, C, or D, the correct choice is E. The final answer is $\boxed{\text{E. No Correct Option}}$.