A rock concert is being held in an open field. Two loud speakers are separated b

Question

A rock concert is being held in an open field. Two loud speakers are separated by a distance of 5.3m. As an aid in arranging the seating, a test is conducted in which both speakers vibrate in phase and produce a 86-Hz bass tone simultaneously. The speed of sound is 343 m/s. A reference line is marked out in front of the speakers, perpendicular to the midpoint of the line between the speakers. Relative to either side of this reference line, what is the smallest angle that locates the places where destructive interference occurs? People seated in these places would have trouble hearing the 86-Hz bass tone.

Explanation / Answer

the condition for destructive interference is d * sindark = (m + (1/2)) * (m =0,±1,±2,.................) when m = 1 then d * sindark= (1 + (1/2)) * =(3/2) * or sindark= (3/2) * (/d) or dark= sin-1[(3/2) *(/d)] = (v/f),v = 343 m/s and f = 86-Hz d = 5.3 m

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