Domande risonanza en
From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.
| AI-translated from Italian. Original page: Domande_risonanza |
How does the body of a string instrument make the sound produced by its strings louder?
Active amplifiers must not be confused with passive ones. In an active amplifier, such as the transistor amplifier of a hi-fi system, the weak input signal is used to drive a stronger signal, which must be produced by a separate energy source. The shape of the output signal is modulated by the shape of the input signal, while its energy source is separate and independent. It is like opening a dam by turning a tap: the opening of the dam is proportional to the rotation of the tap, but the force needed to open the heavy gates of the barrier certainly does not come from our fingers.
The phenomenon observed in musical instruments, instead, is entirely passive, and for this reason the word "amplification" is perhaps inappropriate. The fact is that the sound produced by a string without a sound box is weaker than the one heard when the string rests on the box. This happens thanks to the phenomenon of impedance matching due to resonance. In essence, all the energy put into the sound box, and only that energy, was produced by the muscular force of the player acting on the strings. However, no matter how much energy is given to the string, it cannot transmit it efficiently to the surrounding air. This happens because the impedances of the string and of the air are very different. In other words, sound cannot pass easily from the string to the air, because it travels at speeds that are too different in the two media. The sound box, however, has a low impedance at certain frequencies (this is the phenomenon of resonance), and can therefore efficiently receive energy from the string and transmit it to the air.
In this process, then, there is no real amplification of energy, only a transformation made efficient by the presence of an impedance matching device. Something similar happens with ordinary antennas: every conductor carrying an oscillating electromagnetic field is a source of electromagnetic waves, but only particular geometric configurations with the right shapes and sizes (precisely those seen in antennas) can radiate electromagnetic energy efficiently.
More details on the pages on
and also
Is it true that a bridge can collapse after relatively mild stresses due to the phenomenon of resonance?
It is true that bridges are affected by resonance. Like all elastic structures, they have vibration modes characterised by natural frequencies. This means that it is always possible, in principle, to excite a large-amplitude oscillation by driving the structure with a periodic external force at the right frequency (that is, one corresponding to one of the natural frequencies). It is of course up to the designers to ensure that the resonances of the structure are properly damped, that is, to provide suitable means of dissipating the energy, so that, even at a resonance, the oscillations do not reach a level that would compromise the safety of the construction.
There are, however, several documented cases, even in recent history, in which unexpectedly large resonances appeared in large structures in response to unforeseen excitations or positive feedback phenomena. It is also well known that military units are generally not allowed to march in step when crossing a bridge (see the sign that appears, for example, at the entrance of the Albert Bridge in London, a bridge opened in 1873).
|
|
What are the possible practical applications of the phenomenon of resonance? Are there any devices that exploit this phenomenon?
A great many devices are based on resonance, both for transforming energy and for manipulating or transmitting signals and information. You will find a description of some natural phenomena, and of some devices in which resonance plays a fundamental role, on the page examples of resonance phenomena.
Is it possible to shatter a glass with only the force of the human voice?
| On average, a level of about 160-170 dB is needed to break ordinary glass, while an opera singer can produce sounds with a maximum level of around 110 dB. However, thanks to resonance, the energy produced by the singer can be concentrated in a single normal mode of a crystal glass, producing oscillations of increasing amplitude. The internal forces arising in these oscillations can easily exceed the internal cohesion of the crystal and break the glass. For a singer, the required power is in any case hard to reach while keeping the glass far enough from the mouth to avoid being hurt by the splinters, whereas it is very easy to demonstrate the same phenomenon with the loudspeaker of a home stereo, or with a musical instrument such as the clarinet, which produce comparable sound pressure levels. |
The resonance wavelength of an open tube is equal to twice its length. Is it possible to build a smaller resonator with the same frequency?
In a sound tube (such as the body of a wind instrument) all the air inside the tube takes part in the sound oscillation. The two fundamental properties that make the oscillation possible are inertia and elasticity (see the page oscillating circuits, or analogies in physics for the electrical analogues). The inertia and elasticity of the air are distributed along the whole tube. For this reason the system is said to have "distributed constants". The electronic analogue of this system is the receiving or transmitting antenna.
In a system with distributed constants, the wavelength of the oscillation is of the same order of magnitude as the size of the system. This direct relation no longer holds if we consider a system with "lumped constants", that is, one made of elements each having one property clearly dominant over the others. Such elements are very common in electronics, which commonly deals with components such as capacitors and inductors, characterised mainly by capacitance and inductance respectively, rather than having a mixture of the two properties in comparable amounts.
When a system has "lumped constants", its physical size no longer matters for calculating the resonance, which ultimately depends only on a suitable combination of the constants that determine its elasticity and inertia (or capacitance and inductance in the case of electrical circuits; see for example the discussion in speed of sound).
In electronics, for example, antennas that are fairly small compared with their working frequency can be built by adding a suitable inductive load (a coil) along the dipole. The same is possible in acoustics.
A typical lumped-constant system is the Helmholtz resonator. See the dedicated page for details. Here, in answer to the question, it is enough to note that a Helmholtz resonator has a fundamental resonance frequency much lower than that of a sound tube of the same length.
