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I have been wondering if there are certain media (for instance glass, air, foam, etc.) which are peculiar given their chemical composition and/or structure allowing them to filter out mechanical waves (examples include: sound, vibrations) of high or low frequencies. Do these exist? Could I please have some examples?

The less abstract example: I tend to notice the bass of the music booming over from the car next to me when I am stopped at a red light. I do not know if this is due simply to the amplitude of those low frequency components or whether there is mechanical filtering at play (suppressing the higher frequencies). This is the source of inspiration for asking my question.

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    $\begingroup$ There is something about resonant frequencies but that is more like a band-pass filter $\endgroup$ – ratchet freak Sep 7 '15 at 15:48
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In a more general sense, the electrical concepts of inductance, capacitance and resistance are equivalent to mass, spring constant and friction in the mechanical world. Voltage becomes force and current becomes velocity.

For example, the suspension in a vehicle is a carefully-tuned low-pass filter that uses the mass of the frame and body, the springs on the axles and the shock absorbers to "block" the high-frequency vibrations from the road from being coupled to the passengers and cargo inside.

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Yes, for sound specifically there is a term called "acoustic impedance" that, just like electrical impedance, is frequency dependent. Acoustic impedance results from the acoustic wave equation, which takes the same form as the electromagnetic wave equation.

So any solid has an acoustic impedance just like every conductor has an electric impedance. Acoustic wave transmission depends on angle of incident and the frequency content, with the material impedance attenuating certain frequencies. Ducts act like waveguides, you can make acoustic resonators, etc. - there are a ton of parallels because the underlying equations are almost identical.

Just like electrical impedance matching results in maximum electrical power transfer, acoustic impedance matching results in maximum acoustic power transfer. That's what ultra sound jelly is used for - impedance matching between the wand and skin.

This can be used in reverse - intentional impedance mismatching results in reflected waves and very little acoustic power transmission. There is actually a line of drywall designed to exploit this to prevent/minimize the "noisy neighbor."

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There are analogs to filters in lots of mechanical systems. In fluid systems prone to pressure spikes perhaps because they use a fixed displacement pump, an accumulator will be used to filter out those spikes to prevent damaging other parts of the system.

A vibration isolator acts in much the same way. Sometimes they're used as is. Other times, for more critical applications, they're designed to filter specific frequencies, like the rotational speed of a motor or a pump, to filter those out and limit or prevent that energy from exciting the surrounding structure. That's done by controlling both the geometry and the material properties of the isolator. One of my first projects out of undergrad was designing just such a mount for a small pump motor.

Another mechanical filter is a tuned mass damper. Typically these are found inside skyscrapers and are intended to limit the movement of the building due to earthquakes. The same idea has been applied to appliance motors as well, where a metal "lollipop" is cantilevered off the side of the motor. The resonant frequency of the mass and rod are matched to the operating frequency of the motor. The result is that when the motor turns, the energy at the motor's operating frequency goes into making the mass vibrate in the air instead of transmitting it to the structure of the appliance where it will be radiated as sound.

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