Answer:
λ = 5.65m
Explanation:
The Path Difference Condition is given as:
δ=[tex](m+\frac{1}{2})\frac{lamda}{n}[/tex] ;
where lamda is represent by the symbol (λ) and is the wavelength we are meant to calculate.
m = no of openings which is 2
∴δ= [tex]\frac{3*lamda}{2}[/tex]
n is the index of refraction of the medium in which the wave is traveling
To find δ we have;
δ= [tex]\sqrt{70^2+(33+\frac{20}{2})^2 }-\sqrt{70^2+(33-\frac{20}{2})^2 }[/tex]
δ= [tex]\sqrt{4900+(\frac{66+20}{2})^2}-\sqrt{4900+(\frac{66-20}{2})^2}[/tex]
δ= [tex]\sqrt{4900+(\frac{86}{2})^2 }-\sqrt{4900+(\frac{46}{2})^2 }[/tex]
δ= [tex]\sqrt{4900+43^2}-\sqrt{4900+23^2}[/tex]
δ= [tex]\sqrt{4900+1849}-\sqrt{4900+529}[/tex]
δ= [tex]\sqrt{6749}-\sqrt{5429}[/tex]
δ= 82.15 -73.68
δ= 8.47
Again remember; to calculate the wavelength of the ocean waves; we have:
δ= [tex]\frac{3*lamda}{2}[/tex]
δ= 8.47
8.47 = [tex]\frac{3*lamda}{2}[/tex]
λ = [tex]\frac{8.47*2}{3}[/tex]
λ = 5.65m
