A rock concert is being held in an open field. Two loudspeakers are separated by

Question

A rock concert is being held in an open field. Two loudspeakers are separated by 8.00 m. As an aid in arranging the seating, a test is conducted in which both speakers vibrate in phase and produce an 70.0-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 70.0-Hz bass tone

Explanation / Answer

Given that

the separation between loud speakers, d = 5.3 m

The frequency, n = 72 Hz

velocity of sound, v = 343 m/s

So the wavelength, = v/n = 4.76 m

the condition for destructive interference is

d sin = (m + (1/2))

when m = 1 then

d sin = (1 + (1/2)) = (3/2)

sin = (3/2) (/d)

= sin-1[(3/2)(/d)]

= sin-1[(3/2)(4.76/5.3)] = 36.8

So the required angle is 36.8 deg

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