# Problem in determining constructive or destructive interference of sound waves

if two speakers are separete from each other by 5.25m and an observer is 50m away in the same line that on of the speakers. What type of interference exist?

The speakers are in phase and have a frequency of 1.5khz.

I have problems to resolve this exercise. The formulas for destructive and destructive sound waves are not giving integer numbers.

$$\frac{diff.}{\lambda}=m$$

Constructive: $$\frac{50.274-50}{0.2287}=1.198$$

Destructive:

$$\frac{50.274-50}{0.2287}-\frac{1}{2}=0.698$$

It's not giving me an integer number. So, what kind of interference is this?

• It is in between a maximum and a minimum and nearer a . . . . . May 15, 2017 at 16:20
• This also depends on the frequency of the speakers, how did you select $\lambda$? May 15, 2017 at 16:21
• @caverac i just added the frequency, sorry. May 15, 2017 at 16:24
• @Farcher to be constructive? May 15, 2017 at 16:25
• @exsnake I would say so May 15, 2017 at 17:11

Do this by looking at the phase difference due to the path difference. When the phase difference is less than 120° ($\frac{2\pi}{3}$) the sum of the two (initially equal) amplitudes will have a magnitude greater than the individual wave; when the difference is greater, the result will be a lower amplitude.
This diagram might make that a bit clearer. In it, we have $A_1$, the amplitude of the first wave, with a reference phase of 0°. When we add it to $A_2$ with a phase difference of 90°, the resulting vector is greater than the original. But when we add it to $A_3$, with a phase angle greater than 120°, the resulting vector is shorter.
• I see, thanks for the explanation. Applying this to my question. The path difference is $0.274$ so the phase difference while be $\frac{(2\pi)0.274}{0.2287}=7.53 rad$? In this case in not completely constructive interference? May 15, 2017 at 17:42