Physicits! Interesting question about Resonance / Sound

engstrom0304 · 1 Jun 2013 at 18:33

Hi guys,

If you imagine a violin... The vibration of the string on its own (not attached to the violin body) would be barely audible... The minimal sound you would hear would be the string's vibration and, very little, the vibration of the air around it which has been set in motion by the string.

If you now consider the string attached to the violin, the sound is much louder. This is because the string's vibration is transferred to the body (via a sound post ). The body vibrates, which causes the air pressure inside the body to oscillate and so the air vibrates also.

The sound is louder because more air particles, and the body, are vibrating.

The natural frequencies of the air, the body and the string all overlap so resonance occurs...

Here is the question...

If the sound is made much louder simply by attaching the string to the body then where is this extra energy (kinetic energy of the oscillating particles) coming from? It seems that there is something for nothing here?

The textbook definition for resonance is that when the driving frequency (the string) matches the natural/resonant frequency of another object (the body/air), the amplitude/energy is maximised.

EDIT: I do know how to spell "Physicists" btw!

panyan · 1 Jun 2013 at 18:39

engstrom0304 said:
If the sound is made much louder simply by attaching the string to the body then where is this extra energy (kinetic energy of the oscillating particles) coming from? It seems that there is something for nothing here?

As I understand it, the energy given to the string is the same.

If it were isolated the string would have all the energy to itself so it would vibrate at a higher frequency and for longer (perhaps)

But because it is attached to the violin body that system shares the energy so if you looked just at the string it would vibrate for less time at a lower frequency.

We know that strings arent played in isolation so the string is tuned on the body to give the correct note.

engstrom0304 said:
The textbook definition for resonance is that when the driving frequency (the string) matches the natural/resonant frequency of another object (the body/air), the amplitude/energy is maximised.

I think that explanation is too simplified - if i understand it correctly musical notes are just different frequencies so if the above was true, that would mean only one string would be audible as the other strings (which are at diferent frequencies) could not excite the air particles enough for resonance?

Id be interested to hear a proper physicists take on this though

anything I don't mind · 1 Jun 2013 at 18:48

Trick question, There is no energy it is resonance, it is the behavior of sound frequency, its natural amplification?

DampDog · 1 Jun 2013 at 18:49

It's not creating "extra" kinetic energy. Think of it as focusing/capturing the energy that's already there. The energy that's put into the string when it's being bowed/plucked is transferred into the sound-post/air close to the string, instead of simply dissipating into the free air. The sound box will have natural resonances at different frequencies. So you may hear the strings natural 2nd, 3rd, etc harmonic.

http://www.phys.unsw.edu.au/jw/strings.html

engstrom0304 · 1 Jun 2013 at 18:57

panyan said:
I think that explanation is too simplified - if i understand it correctly musical notes are just different frequencies so if the above was true, that would mean only one string would be audible as the other strings (which are at diferent frequencies) could not excite the air particles enough for resonance?

Id be interested to hear a proper physicists take on this though

This is another thing that bugs me...

PermaBanned · 1 Jun 2013 at 19:04

Resonance is different to what you're describing. An instrument's strings will sound louder when attached to a body because there's a larger area over which the waves can be transferred to the air. Resonance is about a system oscillating with greater amplitude at certain fundamental frequencies even though the same amount of energy is put in.

MBennett · 1 Jun 2013 at 20:58

You are thinking about resonance frequency incorrectly. Everything has a resonance frequency and is the sweet spot to get maximum energy transference by applying the force at the correct time or frequency.

The example I like to think of is of some one on a swing. To get them swinging as high as possible you push them at their resonant frequency ie at the point at the back end of the swing when they are at the highest and you push them forward. It is obvious, you wouldn't for example go trying to push them forward again and again very quickly right to the point when they at the front end of the swing and keep going as you can see that would result in wasted effort as you would work against the swing. If you actually got scientific about it you could go out with a stop watch and measure the period of the pusher pushing the swing and you would find it is consistent, no matter what the amplitude of the swing is. Applying a force at that period will always result in the amplitude getting greater and greater until resistive forces equal the applied force or the object violently breaks.

Amleto · 1 Jun 2013 at 21:05

OP's premise doesn't really make sense since a string that is not attached to anything isn't going to oscillate.

I don't know anything about violins, but I assume it somewhat focuses the vibrations/noise in particular directions as well, giving the appearance of sound amplification.

crisbduck · 1 Jun 2013 at 21:13

Energy is just transferred more efficiently surely?

MBennett · 1 Jun 2013 at 21:13

Oh permabanned is correct about the body of the violin not actually vibrating at its resonance frequency, it is just a body that is more efficient at transmitting the strings waves to the air than via the string directly. Think about it, the body of the violin will only have 1 resonant frequency, that would make a rather rubbish instrument if it worked like that!

I think maybe you are confused with how stringed instruments work:

The string of any length will want to vibrate its at a resonant frequency when stimulated, the frequency of this is determined by the wavelength between nodes. By placing your finger on the string a node is created and you change the wavelength at which the string vibrates, causing the string to vibrate at different frequency - hence moving your finger up and down the string will result in a range of changing frequencies.

Socaddict · 1 Jun 2013 at 22:07

Actually, violins (and other string instruments) will have multiple resonant frequencies all over the bodies. Variation in thickness of the body, shape, etc. There are some good books on this, and the IoP has some stuff too.

Aod · 2 Jun 2013 at 00:49

A violin string that's say, strung between two rubber posts and made to vibrate with the input of x newtons of deflection will vibrate on its own in the air with minimal transference of energy to the surrounding air because the string alone has very little surface area.

A violin string strung on a violin will create a louder sound even when the same x newtons of deflection is applied to the string. The string runs over a sound-board or post which is mechanically connected to the Violins body. The resonant vibration of the string will cause the sound-board to vibrate at the "same" frequency (which would not be its' resonant frequency) which will cause the violin body itself to vibrate similarly.

The body of the violin has many many orders of magnitude more surface area which means it will very effectively transduce vibrations into pressure waves in the air as sound. This greater conversion of vibration (which is a form of stored energy) is largely responsible for the greater volume.

You have to understand that, even though the energy input into the two strings was the same, the violin-mounted string dissipates energy into the sound-creating parts of the violin relatively quickly, which is the conservation of energy re. the greater audio volume.

You would see, if you conducted this experiment, that the string on the violin would cease vibration much sooner than the string mounted between two vibration-isolating posts.

The Violin also creates greater volume than it otherwise would as a result of the shaping and enclosure of the violin which amplifies certain harmonics and frequencies of the audio resulting in greater efficiency of audio creation, hence, greater volume. This is why different sized Violins have different "tones".

Sorry if this isn't the clearest, it's late, I've been up for a while and one of my fingers has a sore cut on it which is making typing difficult