Properties of Waves and how they relate to Music

[avocadogirl]

I'm an undergraduate physics major and, I teach an acoustics lab to undergraduate music majors.

I've tried researching the experiments to find explanations of their relevance to these music majors but, this sort of course does not seem to be extremely common, one in which the physical principals behind sound are tied into the applications to music.

So far, they've covered experiments which investigate Hooke's law and elasticity (with springs), simple harmonic motion (with springs), and wave motion (where they converted rotational motion into wave motion). I lose them when I just start talking about waves but, I'm really floundering to explain any connection between the experimental procedures or objectives and the purpose as is pertinent to a musician.

I continue to fall back upon the redundant, "Sound travels in waves!" And, I don't think that's helping.

Would anyone be inclined to offer some more insightful connections between sound and Hooke's law or, sound and simple harmonic motions or, sound and wave motion? Even if you want to explain these physical principals within the context of the electronics used in the music industry, I would really appreciate it because, I feel I'm doing them an injustice to expect an understanding of the objectives and theories when I, myself, can offer no informative explanation. I can't, in good conscience, just let them monotonously run through the experiment without some evidence of their understanding.

Thanks to all who read and contribute!

 

[DeShark]

Well, i think the importance of learning about how sound propagates is important, but is hardly the be all and end all. Obviously sound is all about vibrations (of strings, of air inside wind instruments, of skins on a drum, etc). These vibrations can take on discrete frequencies (known as harmonics) if the waves are forced to be null at certain boundaries (the ends of the strings on a guitar, the point of contact of the skin of a drum with the cylinder itself, the open hole of a trumpet [confusing as this may be]).

These harmonics obviously have great importance for music as any sound can be created from a superposition of these frequencies cf. Fourier analysis. As such, if we can analyse the dominant harmonics made by an instrument, we can recreate the sound using computer software. Additionally, if they want to study sound damping or any other forms of sound engineering, I think it's important that they understand these basics.

As for hooke's law, it explains why, when the strings on a violin are tightened, the resonant frequency of the string increases and hence the acoustic pitch increases.

 

[avocadogirl]

Okay so, regarding hooke's law, would you look at the strings on a stringed instrument like tightly wound springs, with spring constants as a material property. Then, when you exert a force on the string, tightening it, could you calculate the effects upon the frequency by relating the spring constant of the string to the force?

The students were given an equation where the could relate frequency to a spring constant by 1/2(pi) multiplied by the square root of (the spring constant divided by a component of the force acting upon the spring).

?

The next experiment has to do with longitudinal impulses in a spring. Any suggestions?

But, thank you sir, immensely, for the reply. That will be of an enormous assistance.

 

[DeShark]

Well, hooke's law (F=-kx) gives the relation between the force applied, the mass and the position of an object. From this, you can find the force acting to restore the mass back to its equilibrium position. This gives a resonant frequency, related to the mass and hooke's constant. In a string, hooke's law can be used to derive the wave equation. See http://en.wikipedia.org/wiki/Wave_equation#From_Hooke.27s_law

Thus, it can be seen that hooke's law leads to wave motion, which in turn leads to sounds.
Additionally, the wave can be broken down into normal modes (harmonics), which each have their own frequency.

As for longitudinal oscillations, I'd be thinking more in terms of pressure variations in a wind instrument. Using a slinky, you could say that the areas of the slinky which are closely spaced are analogous to areas of space with high pressure. Again, standing waves can be formed, leading to the same harmonics. I'm sure there are more applications than these to music, but these are all I can think of.

 

[Cvan]

Teach them about wave diffraction and show them the connection between sound waves going around a corner compared to light going around a sharp edge. i.e. why you can hear a marching band down around the corner! Interference of tones and signals, superposition of waves leading to that difference in pitch wavy throbbing they hear when two different tuning forks are set up next to one another.

For an introduction personally the most interesting part of acoustics related to wave properties are their propagation through different mediums, and how they move around in a room and past corners, reflect off the blackboard behind you. Another example, how far can you hear someone at the end of a hall from you compared to outside? Can cover all the elements of a room with good sound quality somehow, :P.

 

[DeShark]

Interference of tones and signals, superposition of waves leading to that difference in pitch wavy throbbing they hear when two different tuning forks are set up next to one another.

This is probably the most useful application I have found when applying my physics to my guitar. Tuning. I'm forever listening for that wobble when tuning my guitar by ear. Just adding two sine waves with slightly different frequency (Probably best to have a pre-drawn illustration to demonstrate the point) shows the interference, producing beats. It is these beats that you hear when tuning.

See:- http://en.wikipedia.org/wiki/Beat_(acoustics )

 

[amezcua]

avocadogirl Just the person I need Have a look at my topic that I started in the following site;
" Violin Forum Leif Luscombe"
The topic is "Control of Interference by Stradivari and Guarneri".
I have played violin since 10 years old and made six violins.I got into hot water for asking a question and had a severe telling off. However if you now look up the words interference and violins -----There it is .-------------------I`ve made my mark in history! I am Amezcua.(Not the guitar maker though). Lots of beautiful violin maps to see.