Interference Between Two Speakers -- Real Life Version of a HW problem

[Albertgauss]

Hello,

Many of you are familiar with the homework problem that goes like the below, and though straightforward to solve in most general physics homework sets, I need to help getting it to work, which is not so easy in real-life.

Consider two speakers separated by 2.0 meters. Find the points along the path from one of the speakers where destructive or constructive interference occurs. The frequency is 1000 Hertz.

The picture and calculations are attached in the jpeg “Slide 1 and 2" for Problem and Solution.

I reproduce here the N’s (Dest), M's (Cons) and X’s (position from first speaker on a line in meters) for which destructive interference should occur.

N X where Dest occurs M X where Cons occurs

n = 1 --> 1.9 meters = X m = 2 --> 1.3 meters = X
n = 2 --> 0.88 meters = X m = 3 --> 0.6 meters = XThe jpeg “Setup” shows the equipment I use and I list the equipment below.

two Pasco 60 Watt Speakers
Both speakers are driven by an AFG1022 Textronix Function Generator, with the intent to drive them at the same time
The microphone is USB, Fifine Company
The waveform software is “Audacity.” which is freely downloaded

Bascially, I move the microphone along the direction “X” in the photo “Setup.jpg”. I move it slowly so that is why the waveforms look stretched out. I move the microphone continuously and slowly, but only barely can I get discernible humps and valleys as maxes or mins. I did also try moving it quickly, but my results were no better (not shown). Lots of times, the points of destructive or constructive interference don’t match very well.When I move the microphone to the X values above, you can see the waveforms of what I get in the following jpegs. “desNeq1.jpg” shows that, when I moved the microphone to 1.9 meters, I got a hint of the destructive interference that I should. However, when I moved the microphone to 1.4 meters, I got a destructive interference I did not predict. These waveforms are not very clear however.

In the jpeg “ConsANDdest.jpg”, you can see that, for constructive interference predicted at 1.3 meters, I actually measure a MIN but not a MAX, as I was supposed to. When X = 1 meter or so, I got another unpredicted MAX. For X = 0.8, I do predict a MIN there, but what I measure is barely convincing.

How could I change my situation/setup so that I can find easily the points of constructive or destructive interference for this problem? I checked my math several times, and I am certain the calculations are right. Would the changes be a lot or a little, expensive or cheap in equipment? What is making my data so unclear? Could reflections in the room itself cause a problem and should this be done outside? I had assumed that since this homework problem appears so often in general, lower-division physics classes, it would be easy to reproduce. Certainly not the case and I’m looking for suggestions on how to improve this, if it can be.

 

[spareine]

In my experience too, interference experirments with two speakers are somewhat disappointing. My best results were at 3.5 kHz (λ = 10 cm) with two small audio speakers, holding one of them in my hand for easy displacement, and detecting interference maxima and minima by ear. The distance between successive maxima was about 10 cm, in the axial direction and in the lateral direction.

I think the problem of interference experiments with two speakers is that multiple mirror images of the sound sources appear due to reflection of sound on hard surfaces, such as a table and the case of each speaker. Due to the many sources there is no completely destructive interference in the minima, and the location of minima and maxima is more complicated.

 

[berkeman]

I think the problem of interference experiments with two speakers is that multiple mirror images of the sound sources appear due to reflection of sound on hard surfaces, such as a table and the case of each speaker. Due to the many sources there is no completely destructive interference in the minima, and the location of minima and minima is more complicated.

Agreed. There was a very nice setup at the Exploratorium in San Francisco many years ago with floor-standing 1m high speakers placed about 15m apart, and the sound was around 600Hz, IIRC. The beats were very apparent when you walked in one direction, and you could walk at some rate in the other direction and not hear any beats.

The two speakers were fairly well isolated in the middle of a carpeted floor on the 2nd floor, without any reflecting objects nearby (except people walking around).

https://www.exploratorium.edu/

https://www.exploratorium.edu/video/full-spectrum-science-interference-beats-0

 

[CWatters]

+1

Constructive interference "only" doubles the amplitude at best. Less in your set up if the speakers are somewhat directional. So any reflections that "fill in" the areas of destructive interference can significantly reduce the difference in volume between the two locations. Try it outdoors if weather permits.

 

[CWatters]

Re the unexpected node/destructive interference at 1.4m...

The wavelength of 1000Hz is about 0.34m at 20C. I noticed that if you substitute x=1.4 into the equation for the path difference

Sqrt(X² +2.25) - X

It works out at about 0.65 or approx 2λ

But that means that n in (n+0.5)λ would have to be 1.5 which is not correct for a node (destructive interference).

So I wondered if both speakers are in phase? It's very easy to accidentally swap the connections over so one is going in when the other is going out.

Worth checking if not already done but I suspect that if they weren't in phase you wouldn't get a node at 1.9m.

 

[Albertgauss]

I understand. I didn't realize just how hard this could be. You all have fantastic suggestions. I'll check the phase of the audio speakers. I didn't do that, but it is worth exploring. Good point by CWatters. The SF exhibit sounds really good, but I'm not sure I can do that here. I did try 600 Hz, coincidentally, but without a setup like SF its no surprise after reading this why my 600 Hz didn't work. I could relocate to a room without furniture; that is possible.

I may try one other thing, this inspired by sparine. Now that I realize there are reflections all over, would sound absorbing materials work? Like anything, the sky is the limit with enough money, but I could get some of this, but maybe not enough to cover a whole room. It will take me a while to try that because I don't have any sound absorbing materials yet, and I am only beginning now to think of how I can acquire some. If possible, would this be a good route to follow, or is it I'm still over my head even with conventional sound absorbers?

 

[CWatters]

Old blankets or curtains hanging up might help a bit.

 

[robphy]

By the way, what are the specific characteristics of your microphone? (cardioid vs omnidirectional, etc...)

 

[Borek]

Just occurred to me: the simplest thing to do is probably to put the speakers on poles, to minimize reflections from the table top.

 

[robphy]

From the photo, I'm worried about the direction that the microphone is facing.
One could also put the microphone (suitably directed) on a cart and use a ranger to measure its position, possibly making an amplitude-vs-position graph.
If you position the track at various distances from the line of speakers, then sweep across, you can try to make a crude map of amplitude-vs-2Dposition (e.g. to find nodal lines).

 

[Tom.G]

Like anything, the sky is the limit...

That triggered a spark. Do the experiment under the sky, i.e. outdoors in a quiet location. (It's quieter at night too.) Perhaps in a nearby park. The grass would act somewhat as a sound absorber. Use an Uninterruptable Power Supply (UPS, battery backup) for power if needed (you will get perhaps 20 minutes of run time, depending on the load). Or use an AC inverter that runs from your car.

Cheers,
Tom

EDIT: You might also find some calculations easier if you use a frequency of 1,150 Hz. That way one wavelength is 1 foot. (wavelength varies a bit with temperature)
OOPS! I see you are using meters, not feet, 350Hz for 1 meter wavelength.

 

[Rive]

Pick a wavelength which is bigger (at least twice as big) than the diameter of your speakers.

 

[spareine]

Or pick speakers that are smaller than the wavelength of choice. I would think λ = 10 cm is convenient, so pick speakers smaller than 5 cm. You don't need fancy speakers to produce a 3.5 kHz tone.

 

[Albertgauss]

Wow, these are great suggestions! Some are easy also! There's really a lot more I can try. I really thought I was at a dead end.

Easiest for me to try next is put the speakers on poles, use the curtains (or get some other sound absorbers), find a room without furniture, though outside in a park is hard because its really rainy right now and I would need more power than 20 mins, indeed, what I reported to you all in this post took several hours.

I admit I didn't get up past 1500 Hertz because I didn't think anyone would do that, go at much higher frequency, but I realize I was wrong, but that is also easy to try. I stopped at 1500 Hz because it started to bother my ears but I can get earplugs for the 3.5 kHz.

I can get smaller speakers. Good point about that. I don't have them right now, but they are obtainable.

I think the microphone is omni-direction and I attach a picture of it. I don't know what a cardoid mic is, but I am alerted now that there may be microphones much better for this kind of experiment (indeed, my only initial choice for a mic was that it was USB) that I need to research. If you know of something obvious about a better mic for this setup, let me know.

A wavelength bigger than diam of speakers, I can do that. I remember now, at least for light, one approx is that the sources are much closer than the point of interference. I will need a bigger room. The problem I encountered with the speakers too close together (~ one meter) is that m's and n's integers that become possible steadily decrease. I was hoping for an effect where I could see m=6,78, etc. With speakers close together, for this problem, you only get "m" or" n" is only possible for 1 or 2.

Also, on which way I pointed the speakers, I pointed the one farthest from the setup at where I held the mic, hoping that would help. Sometimes the far mic pointed parrallel to X, sometimes it was aimed directly at X. Neither way was obviously better that I could tell.

I tried Robphys's suggestion crudely and without much confidence before this post because I wasn't getting anything obvious sweeping the microphone in 2-D. It took a lot of time and the tabletop was in the way. Putting speakers are on poles, however,--which I haven't tried----gives new life to this suggestion as the table would be gone and I could move around the speakers much easier.

Sorry it takes me a day or two to get back. Just busy, but I am still paying attention.

 

[Rive]

I didn't get up past 1500 Hertz

I think you have to go for lower frequencies, not higher. For higher frequencies, even the size of your microphone might be problematic - it just won't fit into the 'quiet' or 'noisy' spots any longer and what it'll pick up is an area average according to its size.
About the size of the speakers: at the point when their size becomes comparable to the wavelength the distances you are calculating with will become fuzzy (every spot of the speakers will has different distances from the spot you are measuring).

Worst case with speakers big enough you can get interference even from just a single speaker... And with interference fields overlapped - well, that's not a good setup.

 

[Tom.G]

The microphone manufacturers web page say "Exclusive designed omnidirectional capsule captures clear sound."
(bold added)

Cheers,
Tom

 

[sophiecentaur]

There are a good number of useful comments here. I agree that taking the experiment outside could reduce the effects of reflections. Rooms in general are poor places for acoustic tests. The reviewers and sellers of hi fi seem to ignore this when quoting flat frequency responses of their wares.

With an omnidirectional mike (regular mike pointing upwards) or a mike in a vertical, open ended tube, you should be able to get a fair standing wave pattern along the line joining the speakers (or just off the line). The direct sound from the speakers will dominate there and you can hope for a couple of convincing nulls near the mid point.”
I have had more success from an ultrasound source and a pair of slots. Young’s slits in effect.

 

[Ketch22]

Sorry about the delay in my getting on this thread. Are you still projecting this idea? I have had good results doing reinforcement projects for demonstration. One of the most important points is that humans have Binaural hearing. Start by calculating the wavelength of the Hz sound you are using. If the "flat" at the peak of the wave is observably shorter than the distance between the ears of a person the reinforcement will be hard to detect as only one ear at a time can receive it. The best projects I have consulted on tends to be around 37-41 Hz. It is also in a very large room or is outdoors so as to prevent echo's. I usually use a single feed from the signal generator this feeds a "parallel wye" splitter that goes to two high accuracy reference speakers. The reinforcements (or cancellations can be mapped and adjusted by the spacing between the speakers.
Moving to a real world application for higher frequency sounds a reinforcement is only heard by one ear at a time. The other is hearing the pitch or possibly even a cancellation. The brain in it's processing will dither the signals and commonly does not register the phenomenon but it registers as a stereo effect.

 

[spareine]

If the wavelength is not larger than the distance between the ears, a simple trick is to put an earplug in one ear.

As a bonus, an experiment that requires someone to walk around with a yellow earplug in one ear is quite memorable.