As Section 17.3 discusses, high-frequency sound waves exhibit less diffraction t

Question

As Section 17.3 discusses, high-frequency sound waves exhibit less diffraction than low-frequency sound waves do. However, even high frequency sound waves exhibit much more diffraction under normal circumstances than do light waves that pass through the same opening. The highest frequency that a healthy ear can typically hear is 2.0 × 104 Hz. Assume that a sound wave with this frequency travels at 342 m/s and passes through a doorway that has a width of 1.2 m. (a) Determine the angle that locates the first minimum to either side of the central maximum in the diffraction pattern for the sound. (b) Suppose that yellow light (wavelength = 576 nm, in vacuum) passes through a doorway and that the first dark fringe in its diffraction pattern is located at the angle determined in part (a). How wide would this hypothetical doorway have to be?

Explanation / Answer

(a)the angle for first minimum is

d sin theta = m Lamda

theta =sin^-1 ( 1 lamda/d)

since lamda = v/f

theta = sin^-1( v/fd)

= sin^-1 (342/2* 10^4 (1.2)

=0.816 degree

(b)

d = lamda/ sin theta = 576 nm/ sin 0.816 = 4.04 * 10^-5 m

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