Refraction of a water wave

Classical Mechanics Level 2

The above is the wave form of a water wave which was generated at the left side of the pool and has a constant frequency. The boundary surface between the deep and shallow areas forms a $45°$ angle with the wave front in the deep area, and a $30°$ angle with the wave front in the shallow area, as shown above. Let $f_d$ and $v_d$ be the frequency and speed of the water wave in the deep area, respectively. Similarly, let $f_s$ and $v_s$ be the frequency and speed of the water wave in the shallow area, respectively. What are the ratios $f_d:f_s$ and $v_d:v_s?$

1:1

and

1:\sqrt{2}

1:\sqrt{2}

and

1:\sqrt{2}

1:1

and

\sqrt{2}:1

1:\sqrt{2}

and

\sqrt{2}:1

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Refraction of a water wave

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