How do speakers produce sound?

[theperfectpunk]

http://imageshack.com/a/img841/50/qgx3.png

The above diagram shows the analyzer of waveform taken from a song. I wanted to know in terms of acoustics how is it that the different frequencies are produced at the same time by the same source. I know about interference but don't know how it works. The same is the case with our ears, we hear different frequencies from different sources at the same instant of time, but our ear drums can vibrate only at one frequency at a particular instant.

How does it work?

 

[rcgldr]

Even though it's just one speaker, different portions of a speaker can vibrate at various frequencies. If the frequency is a harmonic of the speaker, then stationary or moving vibrating nodes (alternating between a "hill" and a "valley") will occur. Other frequencies will produce somewhat randomly moving patterns of nodes.

In the case of an ear drum, the bones transmit the frequencies to the inner ear, and I'm not sure that part of the ear picks up a range of frequencies at the same time.

 

[AlephZero]

A good quality speaker should not "vibrate" (freely) at any frequency. It is being forced to move in an arbitrary way, corresponding to the electrical signal sent to it.

Interference is also irrelevant. I think the OP's problem is having the wrong idea that moving objects always "vibrate at one frequency". That is not true for speakers, eardrums, and most other things in real life. Simple experiments on sound and vibration in physics and engineering are usually special situations that are intentionally easy to understand and measure.

The OP should look at a plot of the waveform of the song against time, not against frequency. It should then be obvious that there is no "single frequency" in the sound.

 

[A.T.]

The above diagram shows the analyzer of waveform taken from a song. I wanted to know in terms of acoustics how is it that the different frequencies are produced at the same time by the same source.

The source just creates some arbitrary signal. It's the analyzer that assumes that the signal is an overlay of sine waves of different frequencies, and approximates the signal this way. But you could just as well decompose the same signal in a different fashion, just like you can represent the same vector in various way as the sum of some other vectors.

 

[rcgldr]

A good quality speaker should not "vibrate" (freely) at any frequency. It is being forced to move in an arbitrary way, corresponding to the electrical signal sent to it.

The point of my previous post is that the entire speaker does not vibrate at all the frequences at the same time. The driven coil moves back and forth according to the source input, but only portions of the speaker respond to the voice coil input, forming nodes of various sizes across the surface of the speaker, depending on the frequency sensitivity pattern of the speaker cone. Generally the higher the frequency, the smaller the average diameter of the vibrating nodes on the speaker surface.

 

[sophiecentaur]

Even though it's just one speaker, different portions of a speaker can vibrate at various frequencies. If the frequency is a harmonic of the speaker, then stationary or moving vibrating nodes (alternating between a "hill" and a "valley") will occur. Other frequencies will produce somewhat randomly moving patterns of nodes.

In the case of an ear drum, the bones transmit the frequencies to the inner ear, and I'm not sure that part of the ear picks up a range of frequencies at the same time.

A sound signal is a variation of the local air pressure in time (and may be different for each ear, of course). This is a description of the signal in the time domain. It is also possible to describe that same signal in the frequency domain, giving the amplitudes and phases of an infinite number of continuous sinusoids. The Fourier transform is a way of taking the information in one domain and transforming it into the other form. Neither domain is any more 'real' than the other. As it happens, our ears analyse the sounds we hear by using a large number of audio filters, each of which which detects a very narrow range of frequencies so you could say that we appreciate sounds in the frequency domain. But, of course, no sound lasts for ever and our brain also appreciates the time variations of the outputs from each of the filters. So, in fact, we sense both frequency and time information.

People are not always aware of the difference between the Fourier transform of any time varying signal (which contains an infinitely dense number of frequency components and the Fourier Transform of a repeating signal (a musical note, for instance), which has components with frequencies that are only harmonics (multiples) of the fundamental (lowest) frequency in the signal. There is a distinct difference but, in practice, signals tend to be analysed to produce a Fourier Series. Even when a signal is not repeated, the Discrete Fourier Transform (DFT) is used, which assumes a repetition. The Fast Fourier Transform (FFT) a further extension of the process (done by computer), which is quicker (and a bit dirtier) than the DFT. Your ear could be said to be performing a Time Varying DFT of what you hear.

 

[AlephZero]

The driven coil moves back and forth according to the source input, but only portions of the speaker respond to the voice coil input, forming nodes of various sizes across the surface of the speaker, depending on the frequency sensitivity pattern of the speaker cone. Generally the higher the frequency, the smaller the average diameter of the vibrating nodes on the speaker surface.

No. In a good quality speaker, the entire cone should move like a rigid piston. Anything else introduces unwanted distortions into the sound.

Of course if you try to reproduce high frequencies with a large speaker, the motion of the cone won't behave like a rigid body. That's why you have two or more loudspeaker cones, with different sizes, to cover the complete audio frequency range.

The fundamental "mass on a spring" resonance of the speaker cone should be below the frequency range it is meant to reproduce.

EDIT: you may be thinking of experiments showing vibrations of a thin flexible circular plate, which do show the nodal circles you are describing. But the reason speakers were tradiitionally shaped as cones, not flat plates, is because a cone shape is much stiffer than a flat sheet made of the same flexible material (e.g. paper).

 

[Redbelly98]

. . . our ear drums can vibrate only at one frequency at a particular instant.

This is not true, and appears to be a misconception on your part about motion and vibration.

A simplified way to put it would be: at a particular instant, the eardrum has a certain position and velocity. If we want to represent the position and velocity as functions of time, one way to do that mathematically is to use a combination of frequencies with different amplitudes.

 

[Philip Wood]

I once read that when (say) a sinusoid is played simultaneously with its second harmonic the ear/brain cannot distinguish between the sounds produced when they are played with different phase relationships. Yet the waveforms produced can be quite different in appearance. Hope you find this as interesting as I do!

 

[sophiecentaur]

In different parts of a room, the phases of the harmonics from an instrument will be different. This can be heard as 'colouration' of the sound but we are not very sensitive to this except under extreme conditions as the individual frequency receptors ( narrow band detectors) do not take account of phase. Non linearity of the ear's processing can mean sensitivity to peaks in amplitude, however. There are techniques in audio processing where the phases are tinkered with to increase the mean level (loudness) yet limit the peak amplitude that an audio amp or RF channel has to handle. Apparently, you can get away with quite high levels of this type of compression before it is too noticeable or objectionable.

 

[mic*]

Maybe this is being really simplistic, but assuming little prior knowledge of wave theory, the first thing deserving mention here is called superposition of waves. This is when multiple waves mix together to create one wave. It doesn't matter if the frequencies are the same or not, they mix.

Waves can interfere to add together (constructive) or they can cancel each other out (destructive).

I'm going to assume an understanding that bass notes are low Hz/frequency (long wavelengths) and that treble is high Hz/frequency (short wavelengths).

Imagine a drawing a nice long wave on a page, it might cycle a few times across the whole page. Now underneath it drawing a very short wave with maybe a hundred little up and down cycles across the page. When the two mix together it would effectively look like the long wave was drawn out of the short one, its couple of cycles would have a hundred little cycles embedded within them.

This mixed wave is what is often displayed as a visual on an analyser, although the pic in the OP is less analog than many representations. The mixed wave is what is sent as an AC electrical signal to the speaker.

The cone of a speaker might move up and down 50 times a second to make some fat bass, but while it is either up or down or in the middle of its stroke, it can be moving up and down 10k per second in addition to this to make some melodic treble notes over the bassline.


...also, I agree with AlephZero's comments about speaker design. Rigid cone.

 

[cjl]

No. In a good quality speaker, the entire cone should move like a rigid piston. Anything else introduces unwanted distortions into the sound.

Of course if you try to reproduce high frequencies with a large speaker, the motion of the cone won't behave like a rigid body. That's why you have two or more loudspeaker cones, with different sizes, to cover the complete audio frequency range.

The fundamental "mass on a spring" resonance of the speaker cone should be below the frequency range it is meant to reproduce.

EDIT: you may be thinking of experiments showing vibrations of a thin flexible circular plate, which do show the nodal circles you are describing. But the reason speakers were tradiitionally shaped as cones, not flat plates, is because a cone shape is much stiffer than a flat sheet made of the same flexible material (e.g. paper).

This desire for the driver to move as a single, solid piston is also why high end speakers use some fairly exotic materials to try to get a very high stiffness-to-weight ratio in their drivers, including (but absolutely not limited to) kevlar, carbon fiber, high end aluminum alloys, and there's even one company that uses a diamond dome for the high frequency drivers in their top end speakers (Bowers and Wilkins).

 

[Pythagorean]

One conceptual problem I see in this thread is that there's no such thing as a frequency at a single point in time. Frequency is a measure of a finite duration time sample. So within five second, a single particle (the speaker as a whole) can display lots of frequencies... as long as they don't have periods longer than five seconds (ok, well 2.5 if you want to get all Nyquist about it).

 

[nitsuj]

Im curious about this like the OP.
The answer I think I understand most were ones that used the term "overlay".

For example "white noise" being an acoustic version of white light.

So it seems the really remarkable part is the speed at which a driver moves at...bringing it all back to the point of cone rigidity, and different sized (inertia) cones for different frequencies.

hmmm...still I'm lost when I try to visualized a cone producing a variety of sounds, like white noise.

So at 100hz does the electricity switches back and forth (+/-) at 100hz, and so does the cone. Now if a 250hz signal is added then what happens? How can that happen?

Strange stuff, but I gottallotta love for speakers, very very dynamic subject (acoustics & reproduction)

 

[Pythagorean]

It's simple, nitsuj, just imagine a wave form of a song. That's essentially what the speaker is doing, moving back and forth. Think of the waveform as a description of the position of the cone.

 

[sophiecentaur]

The design of speakers is not really the issue in the OP, I think. Any ol' speaker will produce a 'sound' for an ear, somewhere in the room, to pick up*. It is just one variation of pressure with time, which, as I wrote before, can be viewed either as just that or, in the frequency domain, as the sum of an infinite number of continuous sine waves. The analysis that the ear / brain makes is a combination of the two.
*I know there are some people who love the imperfections / distortions of old amps and speakers but it's quite possible to mimic the sound of a 'bad' speaker with a 'good' speaker. Anyone at a stadium rock concert is listening to the 'Marshal Sound' from the band's guitar amps, picked up on microphones and amplified by very much more powerful PA systems which can be of very high quality.

 

[nitsuj]

It's simple, nitsuj, just imagine a wave form of a song. That's essentially what the speaker is doing, moving back and forth. Think of the waveform as a description of the position of the cone.

That almost seems too simple!...YAY analog!

Thanks Pythagorean!