Sound of 2 identical horns cancels out?

[dshield55]

I'm wondering if the sound of two identical horns positioned perfectly in front of each other and emitting the same sounds/pressure will cancel each other out no matter what where the only variable changing is how far apart the horns are from each other.

Maybe an example would be two clarinets facing each other and positioned at 2 inches apart versus 5 inches apart. Does it have to be an exact distance apart for the waves to hit each other perfectly out of phase and cancel?

What I'm envisioning is that if the waves are coming from the same direction, they'll eventually hit an equal set of sound waves coming from the opposite direction that's out of phase. Is this wrong?

 

[Ibix]

Kind of. You'd need to control the phase of the emitted sounds to an improbable degree of precision to do it with actual musical instruments, but doing it electronically is routine - it's the basis of those noise cancelling headphones you can buy.

However, note that the conservation of energy will not be denied. The energy of the waves has to go somewhere, and in this case that's off to the side. I guess that noise cancelling headphones redirect it into absorbing materials in the earpiece body.

 

[DrClaude]

This thread might be of interest: https://www.physicsforums.com/threa...ers-real-life-version-of-a-hw-problem.957228/

 

[RPinPA]

I'm wondering if the sound of two identical horns positioned perfectly in front of each other and emitting the same sounds/pressure will cancel each other out no matter what where the only variable changing is how far apart the horns are from each other.

Maybe an example would be two clarinets facing each other and positioned at 2 inches apart versus 5 inches apart. Does it have to be an exact distance apart for the waves to hit each other perfectly out of phase and cancel?

What you want is two waves that are out of phase by 180 degrees. If they have the same maxima and minima at the same time at the source, then they will cancel out at some point where one wave travels half a wavelength farther than the other, or 1-1/2, or 2-1/2, or 3-1/2...

If you are equidistant from the two clarinets, then the sound travels the same distance and if the waves started out in phase, they'll still be in phase and will add up.

Let's do some numbers. Let's use the pitch E4, E above middle C, which has a frequency of about 330 Hz. And let's say the speed of sound is, oh, 330 m/s. So the wavelength is $\lambda = v/f$ = 1 m. Let's say the two sources are 2 m apart and I'm standing in the middle, 1 m from each one. Then the waves will have their maxima and minima at the same time, and they'll add up constructively.

Now let's say I move 25 cm to the left. I'm now 0.75 m from the left source and 1.25 m from the right source. The wave from the right source is now traveling 0.5 m farther, half a wavelength. So it is in a minimum when the wave from the left is at a maximum, and vice versa. They cancel out.

What I'm envisioning is that if the waves are coming from the same direction, they'll eventually hit an equal set of sound waves coming from the opposite direction that's out of phase. Is this wrong?

The analysis is done in terms of path differences. You can arrange it so that in some places in space one wave will travel 1/2 a wavelength farther than the other wave so they'll be out of phase. But there will inevitably be other places where they add up constructively. It's unavoidable. If the two sources are not in the same location, which they can't be, then some points will be closer to one source, some will be closer to the other source, and some will be equidistant.

And then you have to worry about different frequencies. In my example I identified a point which is a null at 330 Hz. But it wouldn't be a null at 400 Hz since the wavelength is different.

 

[dshield55]

If you are equidistant from the two clarinets, then the sound travels the same distance and if the waves started out in phase, they'll still be in phase and will add up.

Let's do some numbers. Let's use the pitch E4, E above middle C, which has a frequency of about 330 Hz. And let's say the speed of sound is, oh, 330 m/s. So the wavelength is $\lambda = v/f$ = 1 m. Let's say the two sources are 2 m apart and I'm standing in the middle, 1 m from each one. Then the waves will have their maxima and minima at the same time, and they'll add up constructively.

Now let's say I move 25 cm to the left. I'm now 0.75 m from the left source and 1.25 m from the right source. The wave from the right source is now traveling 0.5 m farther, half a wavelength. So it is in a minimum when the wave from the left is at a maximum, and vice versa. They cancel out.

What if I'm not in between the clarinets at all? As in I was actually wondering if standing at a perimeter several meters outside the two clarinets... not having to hear them at all. I was hoping they'd cancel out in the middle before bouncing off any walls and making it back to me.

 

[CWatters]

How can something cancel and then bounce of wall? It doesn't work like that. Destructive interference only occurs when the conditions are just right which limits where it occurs to quite small areas. You can have destructive interference in one ear and constructive in the other. Move your head a bit and it changes.

If your PC has stereo speakers give it a go. Search YouTube for Test Tones.

 

[RPinPA]

What if I'm not in between the clarinets at all?

Then wherever you are the phase difference depends on the difference in path length from each clarinet to you.

As in I was actually wondering if standing at a perimeter several meters outside the two clarinets... not having to hear them at all.

There are certainly lots of points in space where the path difference is a half a wavelength, or one and a half, or three and a half, etc.

I was hoping they'd cancel out in the middle before bouncing off any walls and making it back to me.

Well, that won't happen. Destructive interference can happen where you are because the waves happen to be out of phase right at that point. But the waves are still traveling past you and they're going to bounce off things, and the reflected waves will have their own path length which may not work out to destructive interference.

There are many demos and drawings of this on the internet. Here's one.
http://zonalandeducation.com/mstm/physics/waves/interference/twoSource/TwoSourceInterference1.html
You'll notice that the regions where the waves add constructively and destructively are spread all over the "room".

 

[DaveC426913]

Remember that, in all your scenarios, the wavefronts emanating from your two sources are spherical.
They will only cancel where a peak and a trough overlap, and that will only occur in a ring where two spheres intersect.

 

[tech99]

The ear has a log response, so the extraneous echoes must be very small if you want complete cancellation. For instance, if the sound sources are phase locked but amplitudes differ by 10% then there will be 20dB cancellation. This makes the sound appear about a quarter as loud.
I have often demonstrated interference effects with sound in the classroom using small loudspeakers at about 1kHz and driven from the same source.