Two in-phase loudspeakers are 3.0 m apart. they emit sound with a frequency of 490 hz. a microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. at what distance from that midpoint is that first point? the speed of sound in air is 343 m/s.

0.35 m

Explanation:

Constructive interference occurs when the difference in the distance between the two speakers is  

0, λ, 2λ,...  

Here λ = v/f = 343/490 = 0.7m  

The first point of interference is the initial point which would mean the distance is the trivial solution of 0  .

A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found.

Let x be the distance from the midpoint to the next interference.  

This occurs when 1.5 + x -(1.5 - x) = 0.7

so 2x = 0.7 which means x = 0.7/2 = 0.35m