Question

Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with non-reflecting walls, as shown. At a distance of 5.0 m from the center of the slits, a first-order maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly

(A) 0.07 m

(B) 0.09 m

(C) 0.16 m

(D) 0.20 m

(E) 0.24 m

Answer 1

The correct option is: (D) 0.20 m

Explanation:

Since the slits are narrow, we can use m λ = d sin θ, but since θ is clearly large we cannot use the x/L small angle approximation. From the given diagram, the geometry shows sin θ = o/h = 3/5 .. rather than finding θ, we will just use this value for sin θ and plug in … m λ =d sin θ … (1) (0.12) = d (3/5)