Hold a wooden ruler so it protrudes from a desk top. Flick it, and you get a "twang" sound. The ruler acts like a vibrating reed. Blow across an empty bottle's neck and you get a "whistle" sound. If, say, the ruler (reed) is 20mm thick and 80mm long, or the neck (pipe) is 10mm round and a mile long, there would be no vibration. What conditions produce the strongest sound in a vibrating reed or pipe? In a mouth organ, for example, reeds are often the same width and thickness. Only the length is varied. Presumably, one of the reeds will vibrate more strongly than the others, even though the difference may not be noticeable. Conversely, in a keyed organ, flue pipes usually have different diameters and lengths. How do you determine the optimum dimensions for such reeds and pipes?
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$\begingroup$ If, say, the ruler (reed) is 20mm thick and 80mm long,[...] there would be no vibration Wrong. As long as ruler can be modeled as sort of spring with spring constant $k$- it can be imagined as damped harmonic oscillator, and so - it will have frequency and vibrations. Question only if these ruler vibrations produce noticeable sound in the medium that some creatures can hear it (for example bats hear ultrasound, elephants- infrasound). Vibrations of air molecules $\not \equiv$ vibration of ruler. You need to define what exact vibrations you talk about , cause there are many. $\endgroup$– Agnius VasiliauskasCommented May 11 at 9:40
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1$\begingroup$ I stand corrected. I should have said "there will be no sound", not "there will be no vibration". $\endgroup$– MRKCommented May 11 at 13:53
1 Answer
For any object to vibrate, all you need is a mass coupled with a spring. The mass stores energy (and gives it up again) in the form of kinetic energy. The spring stores energy (and gives it up again) in the form of potential energy. when they are connected together and set into motion, they trade that energy back and forth between them in a process we call oscillation.
In the extreme cases you mention, there will be oscillation- but you will not hear it because the number of oscillations per second you get is outside the range covered by your ears.
For a vibrating or oscillating object to produce sound that you can hear, not only does the vibration frequency have to be within the ear's range, it also has to be well-enough coupled to the air to create sound waves strong enough to excite the ear. A drum head has lots of surface area and hence is well-coupled to the air- and when it vibrates, it creates nice strong sound waves. A thin wire can easily be set to vibrate but it is so poorly-coupled to the air that you can barely hear it, if at all... until you connect it to something that looks like a drum head, and then you get a banjo, which you can easily hear.
When the massive object is air (which contains its own springiness), it too can be set into oscillation by shaping the air mass into something that separates out the mass effect and the springiness effect into something where the mass part can bounce off the springy part and oscillate. This is why a bottle full of air can oscillate: the mass of the air inside the neck of the bottle bounces off the springiness of the air inside the body of the bottle and you get oscillations- and sound waves.
The proportions of the bottle neck and body affect the quality of the tone produced, which can either be a fairly pure sine wave with a single dominant frequency (that sounds like a musical note) or a sine wave with a spread of frequencies superimposed (which sounds more like noise than like a musical note).
This is true for organ pipes, strings, metal and wooden bars and so forth, so in each case the proportions of the vibrating object must be carefully experimented with so that when you set it into vibration, you obtain just the tone you desire.
