Sound Waves and Destructive Interference question

[BrooklynBees]

The problem:
Two speakers emit a sound with a frequency of 550.0Hz. At what distance should they be placed to maximize destructive interference?


I have the steps in solving this problem written on my worksheet, and it says that the speakers should be placed at 1/2 wavelength. The thing I don't understand is WHY they should be placed there. Other than that, I understand how to finish solving the problem. I just don't understand what the deal is with 1/2 wavelength.

Thank you!

 

[G01]

You want the sound waves (assumed to be in phase) to destructively interfere? What does this mean in terms of two waves overlapping? i.e. What part of wave 2 must overlap with a crest on wave 1 to cause destructive interference?

You should see (if you draw the waves coming from each speaker to scale) that this overlap will happen if the two speakers are half a wavelength apart.

 

[Moetasim]

I can explain the concept of destructive interference and why speakers should be placed at 1/2 wavelength to maximize it.

Sound waves are a type of mechanical wave that travel through a medium, such as air. When two sound waves of the same frequency and amplitude meet, they can either reinforce each other (constructive interference) or cancel each other out (destructive interference), depending on their relative phases.

The phase of a wave refers to its position in its cycle. When two waves are in phase, their peaks and troughs align, resulting in constructive interference. On the other hand, when two waves are out of phase, their peaks and troughs do not align, resulting in destructive interference.

In the case of two speakers emitting sound waves, the distance between the speakers determines the phase relationship between the waves. When the distance between the speakers is equal to a multiple of half the wavelength of the sound wave, the waves will be completely out of phase and cancel each other out, resulting in destructive interference.

Since the wavelength of a sound wave is inversely proportional to its frequency, the distance between the speakers should be equal to 1/2 wavelength to achieve destructive interference for a sound wave with a frequency of 550.0Hz.

In summary, placing the speakers at 1/2 wavelength maximizes destructive interference because it creates a phase difference between the waves that results in their cancellation. This principle is important in various fields of science and technology, such as noise cancellation and acoustic engineering.