Plane sound waves of wavelength 0.17 m are incident on two narrow slits in a box

Question

Plane sound waves of wavelength 0.17 m are incident on two narrow slits in a box with nonreflecting walls, as shown in the figure below. At a perpendicular distance of 16 m from the center of slits, a first order maximum occurs at point which is 9 m from the central maximum. Using the small angle approximation, what is the distance between the two slits? Answer in units of m. What is the percent error in the determination of the distance between the sits when using the small angle approximation. Answer in units of %.

Explanation / Answer

for small angle aprroximation

y = m*lamda*L/d

given that lamda = 0.17 m

L = 16 m

d = ?

m = 1

and y = 9 m

then

y =m*lamda*L/d

9 = 1*0.17*16/d

d = 0.302 m

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