physics reflection at boundary

👨🏻‍🏫 學術台其他 - 科學

[匿名]

2010-07-12 12:33 am

http://img408.imageshack.us/img408/1612/20100711018.jpg

This material is extracted from tom ducan,
I have a confusion about one concept about reflection at boundary ,
The above link is related to the following passage that i am going to type and I upload it to imageshack as a reference.First let me point out the paragraph which is confusing me.

"Phase changes also occur when longitudial waves are reflected,
as can be shown by sending pulse along a Slinky spring to a denser and less dense boundaries, ie.
to fixed and free ends. At a fixed end a compression is reflected as a compression, at a free
end it is reflected as a rarefaction"

I would like to ask if there is a phase change when reflected at a fixed end,
why a compression is reflected as a compression but not rarefaction?
as far as i know, the phase difference between two compression is 2 pie,
and the phase difference b/w a compression and a rarefaction is pie only
so i wonder if i misunderstand the paragraph?
Plz help me ;(

更新1:

yep i see what you mean. But i want to ask if your answer is valid only in transmittion of longitudal waves? Cause i know that there would be a phase change if string is reflected at denser medium such as a pulse is transmitted from light spring to heavy spring. Are they related?

回答 (2)

eodyam

2010-07-12 7:30 pm

✔ 最佳答案

The determining quantity for in-phase or out-of-phase reflection is the natural frequency of reflector. For example, a denser substance tends to have higher natural frequency (larger k); a fixed end has infinity natural frequency (k=infinity) while a free end has zero natural frequency (k=0).

Vaguely speaking, if the incoming wave oscillates faster than the natural frequency of the reflector. The reflector cannot respond fast enough and there will be a phase lag of pi. So compression become rarefaction. A proof of this is attached below.

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701007110099513873367830.jpg

The phase lag is shown in eq.(3), and can only be zero of pi if there is no friction or resistance.

2010-07-12 11:54:16 補充：
The reflected wave can be thought of being generated by oscillation of the reflector. So if the reflector is oscillating with a phase lag, so does the reflected wave.

2010-07-14 12:29:51 補充：
Yes, this reasoning works for all waves, longitudinal or traverse. The string problem is different from the sound wave problem. A denser reflector causes a phase change for string because a denser medium has lower natural frequency.

2010-07-14 12:33:45 補充：
Recall natural frequency = 2 pi sqrt( k/m ). For string, a denser medium has significantly heavier density (like larger m), and thus lower frequency. For sound wave, a denser medium has significantly stronger inter-atomic interaction (like larger k), and thus higher frequency.

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天同

2010-07-14 1:54 am

You could watch the animation given in the following web-page (that near the middle of the page), which uses sound wave reflection at the open and closed end of a pipe as an example.

http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html

It is clear that a compression will be reflected as a compression at the closed end (simialr to the fixed end of a slinky spring), and a compression is reflected as a rarefaction at the open end (similar to the open end of a slinky spring).

The web-page also gives a short explanation to such phenomenon.

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