Understanding the Fundamental Frequency f1 and Its Role in Sound Waves

[toesockshoe]

My book says "the sound produces by vibrating strings is likewise a superposition of traveling sinusoidal sound waves, which you perceive as a rich, complex tone with the fundamental frequency $$f_1$$. I know this is the normal mode on a string... but sound waves don't have modes right? Also does this mean we can't here strings that vibrate at f_2 or f_3 or so on?

 

[DrewD]

It doesn't mean that we only hear the fundamental, but we perceive the note as the fundamental. You hear all of the other frequencies, but they are perceived as timbre or color. If you strike a guitar string, it vibrates at $f_1$ and many (many) other frequencies. Certain higher frequencies die out more quickly which give the guitar its characteristic tone. To the best of my knowledge it is more of an artifact of our brain that we hear the note as $f_1$. There is obviously a lot more to it that just that, but I think that might start to answer your question.

 

[Simon Bridge]

The string vibrates however it is set up to vibrate, it's motion disturbs the air making sound waves there - which reach your ears.
If the string is vibrating at f2 you will hear whatever that note is (give the limits of hearing). You can set up a string with a multivibrator and see/hear it - there are examples online.

You will have noticed that the string, once set in motion, does not keep vibrating - if you strike a string, or pluck it, what you start out with is a combination of many modes. The higher modes die off faster than the lower ones so you are left with the fundamental.

Other modes may last longer in a musical instrument, that's part of how they are made and it is why different instruments playing the same note sound different.

 

[toesockshoe]

The string vibrates however it is set up to vibrate, it's motion disturbs the air making sound waves there - which reach your ears.
If the string is vibrating at f2 you will hear whatever that note is (give the limits of hearing). You can set up a string with a multivibrator and see/hear it - there are examples online.

You will have noticed that the string, once set in motion, does not keep vibrating - if you strike a string, or pluck it, what you start out with is a combination of many modes. The higher modes die off faster than the lower ones so you are left with the fundamental.

What do you mean once set in motion, does not keep vibrating? that is set in motion, but the vibrations go on. or do you mean if it is set in motion, then you turn off the multivibrator? if you turn it off, then the vibrator is staying still so is pulling the string to equilibrium ... right?

 

[Simon Bridge]

If you pluck or strike a string, as in a musical instrument, it vibrates for a while and then stops.
In fact, pull the string up and release it and you will see, just before the release, the string makes a triangle shape ... it is being set up in an initial condition where the sum of the modes is that triangle. A sort while after release you will see it is basically the fundamental that is left.

 

[toesockshoe]

If you pluck or strike a string, as in a musical instrument, it vibrates for a while and then stops.
In fact, pull the string up and release it and you will see, just before the release, the string makes a triangle shape ... it is being set up in an initial condition where the sum of the modes is that triangle. A sort while after release you will see it is basically the fundamental that is left.

so does each normal mode disappear in reverse numerical order?

 

[Simon Bridge]

It depends on the precise geometry of the setup.
For a string like in the video I'd expect higher energy modes to damp out faster.

The concepts you want to look up are:
resonance
harmonic oscillator: driven and damped.