Chapter 36, Problem 008 Sound waves with frequency 2700 Hz and speed 343 m/s dif

Question

Chapter 36, Problem 008 Sound waves with frequency 2700 Hz and speed 343 m/s diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length 100 m. Th opening, which has a horizontal width of 39.3 cm, faces a wall 100 m away (the figure below). Speaker cabinet Cenral axis Along that wall, how far from the central axis of that wall in meters will a listener be at the first diffraction minimum and thus have difficulity hearing the sound? (Negle Number Units the tolerance is +/-3% Show Work is REQUIRED for this question: Open Show Work

Explanation / Answer

The waves are being diffracted by a single slit, and the formula for the angular distance from the central axis to the first minimum is

sin = /w;

is the wavelength and w the width of the slit.

To find the wavelength, use the relation *f = v
=> = v/f
= 343/2700
= 0.127 m.w is given as 0.393 m

sin = 0.127/0.393

= 18.85º

The distance along the wall is R*tan
= 34.14 m

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