Speakers A and B are vibrating in phase. They are directly facing each other, are 8.0 m apart, and are each playing a 75.0-Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are three points where constructive interference occurs. What are the distances of these three points from speaker A?

The distances of the three points from speaker A is  1). 1.713 m,  2). 4 m,

3). 6.287 m.

Explanation:

Here we have

Speed of sound, v = fλ

Where:

f = Frequency of sound and

λ = Wavelength of the sound

Therefore, λ  = v/f = = 4.573 m

The two speakers are 8.0 m apart

Let X be a point from speaker A on the line where we have constructive interference. Therefore,

(L - X) - X = n·λ

Which gives

Therefore, we have, when n = 0,

When n = 1 we have

, which is the distance from speaker A, since from the nature of the calculation, if we selected X to be from speaker B, then there will be a point of constructive interference at 1.71 m from speaker B

In other words since there is  a point of constructive interference at the mid point, we will have constructive interference at λ/2 on either side of the mid point

Therefore, the three points are;

4 - (4.573 m)/2, 4, 4+(4.573 m)

The distances of the three points from speaker A is

1). 1.713 m,

2). 4 m,

3). 6.287 m.