Can a Longitudinal Oscillator Be Seen as a Standing Wave?

[pinsky]

Hello there!

I was thinking is it possible to observe a simple longitudinal oscilator (lets say a mass on a string) as a standing wave?

Thinking maybe as wave which has a front 4 times than the size of the string. So when we excite the string, we are actually emmiting a wave.


One more thing relatied to oscillations and resonannce. How does an object react when excited by continuous higher harmonics?

Is the gain in the amplitude of oscillation different that of when a body is excited by its natural frequency?

Can higher harmonic also have devastating effects as does excitation by a resonance frequency?

 

[Ken G]

A single oscillator isn't really a wave. It only has one of the two key elements-- a restoring force. The other key element is connectivity-- the work done by the restoring force, instead of being stored in a local potential, has to be communicated to the neighboring environment. That connectivity, or ability to communicate energy, is the key aspect of propagation. So even though a standing wave doesn't propagate, it can be thought of as counter-propagating waves whose propagation effectively cancels, not the absence of the ability to propagate.

Excitation by continuous harmonics is typical. For example, when you blow into a flute, your breath is creating an input over a wide frequency band, but the flute picks out the resonance frequency and all its harmonics. However, some frequencies have more power in the original signal, and some resonate better. Often the fundamental is maximized for both those reasons, but a lot of the design of the instrument goes into the response to the various overtones. So flutes sound different from guitars, both because they are excited by a different type of "power spectrum", and because they respond differently to that excitation. So you are right-- there is an issue of gain that depends on frequency.

As for devastating effects, some time look at the video of the Tacoma Narrows bridge. It was destroyed by a resonance that does not look like the fundamental frequency of the bridge, there appear to be several nodes.

 

[Oscur]

Ken G is right. However, you can think of an oscillator as tracing out the shape of a wave as it oscillates. Analogous to this is the situation of electrical charges which may oscillate, causing the medium they make up to emit an electromagnetic wave.