Could transverse wave on a string could be used to produce sound?

[Jackson Lee]

I feel curious about why we pay so much attention on standing waves on the string. Doesn't transverse wave on the string can't be used to produce sound?

 

[Dale]

It certainly can be used to produce sound. That is how all stringed musical instruments work.

The wave that it creates in the air is longitudinal, but there is nothing preventing a transverse wave in the string from creating a longitudinal wave in the air.

 

[Jackson Lee]

It certainly can be used to produce sound. That is how all stringed musical instruments work.

The wave that it creates in the air is longitudinal, but there is nothing preventing a transverse wave in the string from creating a longitudinal wave in the air.

But I have never seen anything about the topic since then, while nearly every physics books paid much attention on standing waves which surely could produce sound on string and wind instrument. Some of them even state clearly that it is standing waves that produce sound therefore we should make deep research into this topic. And I have found this description:[Those frequencies that are not one of the resonances are quickly filtered out—they are attenuated—and all that is left is the harmonic vibrations that we hear as a musical note.] How do them be filtered out?

Thus, I felt surprisingly when watched that experiment.
But if transverse wave could also be used to produce sound, then why we make so much attention on standing waves instead of transverse waves?

 

[olivermsun]

But if transverse wave could also be used to produce sound, then why we make so much attention on standing waves instead of transverse waves?

Standing waves on the string are transverse waves. The standing pattern is created because there are (transverse) waves traveling in both directions up and down the string and reflecting back and forth between the ends.

 

[AlephZero]

Thus, I felt surprisingly when watched that experiment.

That looks like artefacts caused by the rolling shutter in the camera. http://en.wikipedia.org/wiki/Rolling_shutter It only shows up when the strings are from top to bottom of the picture, not from side to side.

A nice example of how unreal it can make a digital image of a moving object:

 

[olivermsun]

Camera artifacts aside, bowed strings are not filled with standing waves. There are clearly propagating transverse waves.

Edit: Found a reaaaaally slow motion clip here:

 

[AlephZero]

It certainly can be used to produce sound. That is how all stringed musical instruments work.

The vibration of the string doesn't produce the sound directly, The string diameter is tiny compared with the wavelength of the sound in air, so at best you would get a small amount of a dipole radiation from the opposite "sides" of the string. The sound comes from the vibrations of some resonant object (e.g. the wooden body of an acoustic guitar), and they are forced transverse vibrations, since they are usually not at the resonant frequency of the object.

You can demonstrate this by comparing the amount of sound produced by a tuning fork in air (which is inaudible unless the fork is very close to your ear), compared with when it is touching a solid object like a table top and making the table vibrate.

 

[AlephZero]

Camera artifacts aside, bowed strings are not filled with standing waves. There are clearly propagating transverse waves.

This can turn into a debate about semantics. The same motion can be described either as a traveling wave reflected repeatedly from the ends of the string, or a superposition of standing waves of different frequencies (i.e integer multiples of the fundamental frequency). At an elementary level it's easiest to consider just one standing wave, which might explain why the OP's question.

On the other hand, a standard way to make a computer model of the physics of real string and wind instruments (rather than the idealized ones in a Physics 101 textbook) is to use "digital waveguide syntheses" which only uses transient waves.
https://ccrma.stanford.edu/~jos/swgt/

 

[olivermsun]

This can turn into a debate about semantics. The same motion can be described either as a traveling wave reflected repeatedly from the ends of the string, or a superposition of standing waves of different frequencies (i.e integer multiples of the fundamental frequency). At an elementary level it's easiest to consider just one standing wave, which might explain why the OP's question.

I'm not sure it's just semantic. If one is actually looking at some detailed waveforms or high-speed photography of a bowed string, then what one tends to see is a lot of "non ideal" phenomena.

Maybe what I should have said is: "The motion of the bowed string isn't just a bunch of standing waves."

On the other hand, a standard way to make a computer model of the physics of real string and wind instruments (rather than the idealized ones in a Physics 101 textbook) is to use "digital waveguide syntheses" which only uses transient waves.
https://ccrma.stanford.edu/~jos/swgt/

Right. Because the realistic motion of the bowed string is actually pretty bizarre.

 

[Orodruin]

I'm not sure it's just semantic. If one is actually looking at some detailed waveforms or high-speed photography of a bowed string, then what one tends to see is a lot of "non ideal" phenomena.

Maybe what I should have said is: "The motion of the bowed string isn't just a bunch of standing waves."


Right. Because the realistic motion of the bowed string is actually pretty bizarre.

Any wave is a superposition of standing waves. In fact, the slow motion video you linked essentially shows this very well where the amplitude of the higher frequency modes are kept large as long as there is a source and decay rapidly once the source is removed, leaving only the ground state or as good of an approximation to it as is reasonable if accounting for a real non-idealized case. I would say it is definitely a question of semantics.

 

[olivermsun]

Any wave is a superposition of standing waves.

Do you mean: any wave on a string with reflecting boundary conditions?

In fact, the slow motion video you linked essentially shows this very well where the amplitude of the higher frequency modes are kept large as long as there is a source and decay rapidly once the source is removed, leaving only the ground state or as good of an approximation to it as is reasonable if accounting for a real non-idealized case. I would say it is definitely a question of semantics.

The entire point of a bowed string is that there is almost always a time-varying forcing that has a very complicated form. Once you remove the bowing and let the string ring, then all the interesting stuff damps out very quickly and you get something like a first-mode standing wave.

But perhaps I should "bow" to the "idealizationists" since this is really getting beyond the scope of the OP's question?

 

[Dale]

The vibration of the string doesn't produce the sound directly, The string diameter is tiny compared with the wavelength of the sound in air, so at best you would get a small amount of a dipole radiation from the opposite "sides" of the string. The sound comes from the vibrations of some resonant object (e.g. the wooden body of an acoustic guitar), and they are forced transverse vibrations, since they are usually not at the resonant frequency of the object.

You can demonstrate this by comparing the amount of sound produced by a tuning fork in air (which is inaudible unless the fork is very close to your ear), compared with when it is touching a solid object like a table top and making the table vibrate.

Oh, cool, that is very interesting! It makes perfect sense. That must be why you don't get good sounding minimalist guitars or violins without a body.

 

[Dale]

But if transverse wave could also be used to produce sound, then why we make so much attention on standing waves instead of transverse waves?

As others mentioned, standing and transverse are not mutually exclusive categories of waves. You could have a standing wave which is transverse or a standing wave which is longitudinal.

I am not getting into the standing vs traveling wave discussion.

 

[AlephZero]

Any wave is a superposition of standing waves. In fact, the slow motion video you linked essentially shows this very well where the amplitude of the higher frequency modes are kept large as long as there is a source and decay rapidly once the source is removed, leaving only the ground state or as good of an approximation to it as is reasonable if accounting for a real non-idealized case. I would say it is definitely a question of semantics.

Just for completeness, in the real-world situation including damping (not just from the air, but internal to the material of the string and the rest of the instrument), the motion of a "standing wave mode shape" is not necessarily at the same phase at every point on the structure. (And I put "standing wave mode shapes" in quotes, because of course they decay exponentially, unlike undamped mode shapes.)

There are probably two issues here: whether this is outside the scope of the OP's question, and whether it is outside the scope of the OP's math knowledge to understand it at more than a hand-wavy level. The OP had another thread which seemed to want to derive the theory of acoustics starting from the statistical mechanics of a gas...

 

[sophiecentaur]

Oh, cool, that is very interesting! It makes perfect sense. That must be why you don't get good sounding minimalist guitars or violins without a body.

Matching is what counts.

 

[Jackson Lee]

That looks like artefacts caused by the rolling shutter in the camera. http://en.wikipedia.org/wiki/Rolling_shutter It only shows up when the strings are from top to bottom of the picture, not from side to side.

A nice example of how unreal it can make a digital image of a moving object:

Thanks a lot, I got it. But I have another question. How do those frequencies which are not one of the resonances quickly filtered out?

 

[olivermsun]

Well, first of all there are a couple things going on that cause standing modes in a plucked string that are not really "filtering."

If you excite the string by plucking (or most any other method), then the pattern you impose in the string will have nodes (the displacement is zero) at both ends. That's just because the ends of the string are (more-or-less) fixed in place by the "nut" and the "bridge." So you already know that the pattern has to be something like a sum of modes.

The exact modal content will depend only on where you pluck the string (assuming all you can do by plucking is to create a "kink" in the string).

The initial waves will travel away from the disturbance, traveling in both directions (half goes each way). The waves keep reflecting off the ends and so you will observe standing waves (caused by the superposition of waves traveling in opposing directions).

For a variety of reasons, the higher harmonics, which have a "sharper" shape, will die out faster; after a little while you mainly notice the fundamental mode of the string. This is probably the important "filtering" that goes on in the string.

In the bowed string, there is a complicated interaction between the bow and the string. You can imagine the string repeatedly sticking and slipping on the bow hair as the bow is drawn across the string. A key point is that the stick-slip cycles tend to be synchronized with the wave as it returns from the end of the string, so that the repeated forcing by the bow is resonant with the natural mode.

The string also has torsional (twisting) modes, which can have a different wave speed from the transverse modes. The complicated interactions between the torsion and transverse modes and the stick-slip of the bow are a major part of why bowed instruments are difficult to play with a "good" sound.

 

[rcgldr]

update (I thought the op was thinking of the sound produced from the longitudunal component of transverse (traveling) waves.) - The sounds from a stringed instrument do not require standing waves, and "traveling" waves can also generate sound. The sound board on a stringed instrument could also have standing waves at specific frequencies, but generally it will have waves traveling across and around a 2d plane.

For a guitar, standing wave overtone notes can be forced by placing a finger at what will be a node of a standing wave, for 2x, 3x, ... , frequency.

 

[olivermsun]

Note that the bridge on a guitar or similar stringed instruments is oriented perpendicular to the strings. This would seem to imply that it's mostly picking up wave motion perpendicular to the string, but not just standing waves. The transverse (along the string) motion is relatively small compared to the perpendicular motion.

I believe you may be thinking of the "longitudinal" wave in the sting. The transverse wave should be "across" relative to the direction of wave propagation.

 

[rcgldr]

I believe you may be thinking of the "longitudinal" wave in the sting. The transverse wave should be "across" relative to the direction of wave propagation.

That is what I thought the op was asking (bad assumption on my part). I corrected my previous post. There are also longitudinal waves that travel at the speed of sound in the string or wire, but I assume these would produce frequencies way above the audible range.

 

[Khashishi]

Thus, I felt surprisingly when watched that experiment. ?

This is a cool aliasing effect of the camera's shutter (which probably scans across the image vertically) with the string waves. That's why the effect looks different for horizontal and vertical strings. The result is that you get something like a time domain plot of the wave, instead of the usual space domain (when viewing horizontally).

 

[Jackson Lee]

Well, first of all there are a couple things going on that cause standing modes in a plucked string that are not really "filtering."

If you excite the string by plucking (or most any other method), then the pattern you impose in the string will have nodes (the displacement is zero) at both ends. That's just because the ends of the string are (more-or-less) fixed in place by the "nut" and the "bridge." So you already know that the pattern has to be something like a sum of modes.

The exact modal content will depend only on where you pluck the string (assuming all you can do by plucking is to create a "kink" in the string).

The initial waves will travel away from the disturbance, traveling in both directions (half goes each way). The waves keep reflecting off the ends and so you will observe standing waves (caused by the superposition of waves traveling in opposing directions).

For a variety of reasons, the higher harmonics, which have a "sharper" shape, will die out faster; after a little while you mainly notice the fundamental mode of the string. This is probably the important "filtering" that goes on in the string.

In the bowed string, there is a complicated interaction between the bow and the string. You can imagine the string repeatedly sticking and slipping on the bow hair as the bow is drawn across the string. A key point is that the stick-slip cycles tend to be synchronized with the wave as it returns from the end of the string, so that the repeated forcing by the bow is resonant with the natural mode.

The string also has torsional (twisting) modes, which can have a different wave speed from the transverse modes. The complicated interactions between the torsion and transverse modes and the stick-slip of the bow are a major part of why bowed instruments are difficult to play with a "good" sound.

Sorry, what I want to know is why those frequencise which are not harmonics will die out totally, because it seems we never take them into account, but not higher harmonics.

 

[Jackson Lee]

That is what I thought the op was asking (bad assumption on my part). I corrected my previous post. There are also longitudinal waves that travel at the speed of sound in the string or wire, but I assume these would produce frequencies way above the audible range.

Sorry, you might misunderstand my meaning. What I want to know is why those frequencise except harmonics will die out totally soon. For example, harmonics are 50Hz, 100Hz, 150Hz... Then why some others, such as 49Hz or 88Hz will die out?

 

[olivermsun]

Sorry, you might misunderstand my meaning. What I want to know is why those frequencise except harmonics will die out totally soon. For example, harmonics are 50Hz, 100Hz, 150Hz... Then why some others, such as 49Hz or 88Hz will die out?

If the fundamental frequency of the string is 50 Hz then how would you excite a 49 Hz oscillation?

 

[Jackson Lee]

If the fundamental frequency of the string is 50 Hz then how would you excite a 49 Hz oscillation?

Sorry, just omit 49Hz.

 

[olivermsun]

Same question applies to 88 Hz.

My point in my (long) post was that the wave you excite in the string by plucking has to have nodes (zeros) at both ends of the string, so it has to be oscillate at some combination of harmonic frequencies.

 

[Jackson Lee]

Same question applies to 88 Hz.

My point in my (long) post was that the wave you excite in the string by plucking has to have nodes (zeros) at both ends of the string, so it has to be oscillate at some combination of harmonic frequencies.

Do you mean that those frequencies never exist at all?

 

[Jackson Lee]

Same question applies to 88 Hz.

My point in my (long) post was that the wave you excite in the string by plucking has to have nodes (zeros) at both ends of the string, so it has to be oscillate at some combination of harmonic frequencies.

But via Fourier series, there did very possible exist some other frequencies which died out later. It sounds impossible that those harmonics just enough to form initial wave.

 

[olivermsun]

At the moment before you pluck and release the string, there are no frequencies in the string at all. All you do is impose a shape on the string. If you analyze the shape using Fourier series, then all your terms have to look like $\sin (n\pi x/L)$ because the sum of the waves must have a node at each end. Those are exactly your standing modes, which oscillate at harmonic frequencies.

If you could excite a traveling wave on the string by some other method besides plucking, then you could create non-harmonic frequencies. These frequencies would be hard to continue forcing for very long, since your reflected wave would be out of phase when it returned to the forcing point, but sure, you could in principle generate a pulse or a wave packet that propagates up and down the string.

 

[Jackson Lee]

At the moment before you pluck and release the string, there are no frequencies in the string at all. All you do is impose a shape on the string. If you analyze the shape using Fourier series, then all your terms have to look like $\sin (n\pi x/L)$ because the sum of the waves must have a node at each end. Those are exactly your standing modes, which oscillate at harmonic frequencies.

Sounds great, then if it possible to prove this by Am=∫[f(x)sinwx]dx=0