Standing waves in stringed instruments

[reverie1995]

Homework Statement

Hi, I'm currently doing a project on the physics of music, more specifically physics of stringed instruments. I don't really understand how are standing waves generated and used in stringed instruments. Are the standing waves present in the string, in the sound wave, or both?

Homework Equations

The Attempt at a Solution

Just to confirm, the wave traveling along the string is a transverse wave right? And isit right to say that the standing wave in the string causes the string to vibrate? I haven't been able to find much information on this, hope someone can enlighten me:) thanks.

 

[diazona]

I assume you've seen a string instrument play, right? The pattern of motion that you see the string undergoing when it's producing sound is a standing wave. You're correct that it is a transverse wave, since the motion of the string is perpendicular (transverse) to the string itself.

Basically the way string instruments work is that when the player draws the bow across the string, the bow exerts a frictional force on the string. This pulls the part of the string that the bow is touching sideways a little bit. Then that part of the string pulls the parts adjacent to it sideways, and those parts pull the parts adjacent to them sideways, etc. etc. This is a traveling wave. (For another example, imagine - or better yet, actually try this - holding a string a few feet long and shaking it slightly side to side. You'll see a wave traveling down the string, although unless you have the string pulled tight, it won't travel very far) Now, when the wave gets to the end of the string, it can't go any further, so it bounces back. Of course, the bow is still pulling on the string this whole time, so when the wave bounces back, it meets another wave that's on its way up from where the bow is pulling the string. The two traveling waves going in opposite directions make a standing wave. For some more explanation of this, you can look at Wikipedia.

Anyway, the net result of all this is that when you play a string instrument, it doesn't take very long at all to create a standing wave on the string. Remember, this means the string is vibrating side-to-side all the way along its length. (unless there are nodes at certain points on the string - that's something for you to look up) These vibrations cause the string to bump into air molecules, which creates pressure waves, a.k.a. sound waves, that travel through the air much the same way that the waves of vibration travel along the string (although the waves in air are longitudinal, not transverse). That's how the sound reaches people's ears.

 

[reverie1995]

Thanks for the explanation. However, I forgot to say that the instrument I am working on is something like a guitar, and everytime I pluck it it only produces one wave, and there is no wave to meet with the reflected wave, so how does the standing wave come about? Is it because λ=2L, so the standing wave consists of the first half of wave (reflected) and the second half of the wave?
I still have some other queries:
-Does a standing wave cause the wave to "last longer", hence disturbing the air molecules around for a longer period of time, sustaining the sound? If so, is this what resonance is all about?
-I have read that in musical instruments, instead of cancelling each other, the superposition of the two waves are supposed to increase the amplitude. Will the cancellation of waves ever happen in a string where both ends are held?
-Does changing the tension of the string have anything to do with changing the number of nodes in the standing wave, or harmonic?
-Is it true that the more nodes there are, the more waves the are hence having a higher pitch?
Thank you very much:)
(By the way, I am new here, so am I posting in the right forum?)

 

[reverie1995]

whoops sorry, ignore what I asked about resonance.

 

[rdl]

Standing waves in stringed instruments are a result of the interaction between the string and the sound waves produced by the instrument. When a string is plucked or strummed, it begins to vibrate at its natural frequency, which is determined by its length, tension, and mass. As the string vibrates, it creates sound waves that travel through the air. When these sound waves reach the other end of the string, they reflect back and interfere with the original waves, creating a standing wave pattern.

The standing wave pattern is a result of the superposition of the original wave and the reflected wave. This means that the two waves combine and form a new wave with a different shape and amplitude. The points on the string that do not move are called nodes, while the points with the greatest movement are called antinodes. The standing wave pattern is created by the nodes and antinodes, and it is what allows stringed instruments to produce different notes and tones.

So to answer your question, standing waves are present in both the string and the sound waves. The vibration of the string is a result of the standing wave pattern, and it is this vibration that produces the sound waves we hear. The standing wave pattern is what allows for the production of different notes and tones, as the length of the string can be changed by pressing down on frets or changing the tension of the string.

In summary, standing waves are an essential part of how stringed instruments produce sound. They are a result of the interaction between the string and the sound waves produced by the instrument, and they allow for the production of different notes and tones by altering the length and tension of the string. I hope this helps clarify your understanding of standing waves in stringed instruments.