4b: A Few Other Examples of Resonance

Resonance can occur in any system that has a natural frequency. You probably have experienced a rattle or buzz in your car that only occurs at a certain speed. This is an example of resonance; the tires provide a periodic driving force which changes frequency as you change speed. Various parts of the car have different natural frequencies, particularly parts that have come loose. If the driving frequency of the rotating tires matches the natural frequency these parts will vibrate at a larger amplitude, making a buzz or rattle. Here are some other examples.

Video/audio examples:

What is the driving force in this case?

Bridge resonances:

Bouncing.

Twisting.

Tacoma Narrows.

Russian Bridge.

Breaking glass: What are the driving forces in these two cases?

Another video (downloadable).

More singing rod: What is the driving force that makes the rod resonate?

A web page with more examples of resonance.
A description of building resonance as a result of a dance class.

You probably have blown across the top of a bottle to get a note. Different sized bottles make different notes and partially filling the bottles with water also changes the pitch. These are examples of Helmholtz resonators; a container of gas with a single opening that will resonate at a specific pitch. Blowing across the top causes a driving force on the air inside which has a natural frequency due to the ‘springiness’ of the air and the size of the container. As we will see, acoustic stringed instruments such as the guitar consist of a hollow body which acts like a Helmholtz resonator. If you have ever been annoyed by a low frequency sound while driving down the highway with one window partially open, you were experiencing a Helmholtz resonance where the air blowing past the open window caused the air inside the car to vibrate: Here are more details on Helmholtz resonance.

Resonance also occurs in electrical circuits. In fact this is one way a radio receiver can tune a certain frequency. The parameters of the circuit are adjusted so that the circuit has a resonance equal to the frequency you are trying to listen to. With those parameters the circuit has much more current flowing for that particular frequency, thus making current flow for that frequency much larger than any other frequency. Here is a circuit simulation that shows three circuits. The top circuit is being driven below resonance so the current flow is small. The bottom circuit has a driving frequency that is too large. The middle circuit is driven at the resonance frequency of 41.1 Hz and has the largest current oscillations.

You may have heard the word resonance applied in the medical world. Magnetic Resonance Imaging (MRI) is used in medicine to get images inside the body without doing harm to the living tissue. Every different molecule in the body has a different natural frequency of oscillation. Each molecule also has electrical charges on them so that they can be driven by an oscillating magnetic and electric field (an electromagnetic wave). When the driving frequency of the oscillating magnetic field equals the natural frequency of the molecule, the molecule absorbs the energy and undergoes larger oscillations. This absorbed energy doesn’t pass through the body and so is not detected outside after the magnetic field passes through. By changing the driving frequency (the frequency of the electromagnetic wave) it is possible to map the location of different types of molecules in the body, giving a map of the internal structures. This tutorial on MRI gives more details and shows some pictures generated using magnetic resonance imaging.

So far we have been talking about systems that have a single resonance frequency. The peak in the graph above is very sharp which means that driving the system at any frequency other than 2.5 Hz will not produce a very large amplitude vibration. Many systems, including musical instruments, have a wide range of frequencies at which the system will resonate. Several different resonance curves appear in the graph below. Notice that, although there is always a single resonance frequency for any one curve (the frequency of the peak), there are many frequencies near resonance that will cause almost the same amplitude of vibration. The width of the resonance curve is called the Quality or Q-factor. The higher the Q-factor, the narrower the curve and the more selective the system is about what frequencies will excite it into resonance.

resonancesbroad

The mathematical calculation (not given here) of the Q-factor depends on the amount of friction or damping in the system. Less damping means a narrower and higher resonance curve and it also means the frequencies will die away more slowly. An instrument designed with a high Q-factor would resonate loudly and for a long time but only at one frequency. Decreasing the Q-factor by having more damping means the resonance is not as sharp or as loud but it allows the instrument to play many different notes with nearly equal loudness. As we will see, the body of stringed musical instruments demonstrates a trade-off between sharp resonances (high Q) and broad range (low Q).

Simulation exercise 4B (turn in answers on a separate sheet of paper): Resonance in several springs.
Simulation exercise 4C (turn in answers on a separate sheet of paper): Q-Factor.

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