High-frequency sound waves exhibit less diffraction than low-frequency sound wav

Question

High-frequency sound waves exhibit less diffraction than low-frequency sound waves
do. However, even high frequency sond 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 2.0e4 Hz. Assume that a sound wave with this frequency travels at 343 m/s and passes through a doorway that has a width of 1.0 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 = 575 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 the hypothetical doorway have to be?

Explanation / Answer

angle=sin-1(lamda/width)

lamda=v/f ....velocity divded by frequency

=sin-1(v/fw)

a) sin-1((343m/s)/(2.0e4)(1))=0.982 degrees

b) sin(0.982)=lamda/width...w=lamda/sin(0.982)..... (575e-9m)/sin(0.982)= 3.355 e-5 m

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