Radio waves in air and water - difference in path

[Mircro]

Homework Statement

Radio waves of wavelength 12m propagate from the source. The source is on the surface of the water and two waves propagate from it: one through the air and the other through the water. After they both crossed the 100m they find themselves together again. What is the path difference between these two waves? (water refractive index is n = 1.33)

Relevant Equations

$$φ=\frac{2π}{λ}δ$$ $$δ=x_1−x_2$$ $$λ'=\frac{λ}{n}$$

Hello, this is an assigment form the 4th grade high school physics in Croatia, concerning electromagnetic waves.

Radio waves of wavelength 12m propagate from the source. The source is on the surface of the water and two waves propagate from it: one through the air and the other through the water. After they both crossed the 100m they find themselves together again. What is the path difference between these two waves? (water refractive index is n = 1.33)
Solution: 9m

While searching for the solution, I found there are optical and geometrical path, we haven't learn about this different paths in school, so I don't know what is this referred to. I don't understand the meaning of the assignment: what does it mean that they "find themselves together again"?

The part is " what is the path difference between these two waves" is crucial because In my language the question would be find the what is the ""razlika hoda": I don't know what is this term exactly in English so I'll try to explain how it is defined in my textbook:

"Razlika hoda" is the difference in paths that two waves travel from the source to some point in space $$δ=x_1−x_2$$

Then the phase difference is: $$φ=\frac{2π}{λ}δ$$

Hopefully I've explained enough about what the problem is :)

Thank you in advance

 

[kuruman]

I don't know Croatian at all so I cannot clarify what "razlika hoda" refers to. However, I noted that the supposed answer of 9 m is the wavelength of the radio waves in water $$\lambda' = \frac{\lambda}{n}=\frac{12~\mathrm{m}}{4/3}=\frac{3\times 12~\mathrm{m}}{4}=9~\mathrm{m}.$$This is not a difference in any sense of the word that I can think of.

Now the path difference in meters is L₂ - L₁ = 0 because the two paths in meters have equal lengths. Perhaps what is being asked is the path difference where the unit of length is not meters but a wavelength. The wavelength in water is shorter than the wavelength in air which means that you can fit more wavelengths in 100 m of water than 100 m of air. If the difference between the two is what is being asked, then the answer is not 9 and the units are not meters. Something doesn't match or is lost in translation.

Maybe a PF member who understands Croatian can answer this, but I think you should really ask your teacher to explain.