Understanding Standing Waves: Clarity on Conditions

[Amith2006]

Sir,
I have some doubts regarding standing waves. Can anyone who is online now clear my doubts?
For the production of standing waves should the 2 interfering waves have the same amplitude, should they be in phase, should they have the same frequency and velocity? I have this doubt because each book states different conditions.

 

[Astronuc]

Hopefully this helps -

The modes of vibration associated with resonance in extended objects like strings and air columns have characteristic patterns called standing waves. These standing wave modes arise from the combination of reflection and interference such that the reflected waves interfere constructively with the incident waves. An important part of the condition for this constructive interference for stretched strings is the fact that the waves change phase upon reflection from a fixed end. Under these conditions, the medium appears to vibrate in segments or regions and the fact that these vibrations are made up of traveling waves is not apparent - hence the term "standing wave".

http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/standw.html

The amplitude need not be the same, but the wavelengths (frequency) would be, so this also infers the same wave velocity, since the interfering waves must be in phase temporally.

 

[Amith2006]

Sir,
I didn’t understand one thing. You said that the waves will be in phase temporarily. Could u please explain it in detail? Also,can standing waves be produced by the interference of 2 waves of same frequency moving in opposite directions having a constant phase difference? If Yes,will this initial phase difference be maintained always?

 

[al_201314]

This java applet could be of some help too.

http://www.walter-fendt.de/ph14e/stwaverefl.htm

 

[Astronuc]

You said that the waves will be in phase temporarily

No, I said "the waves will be in phase temporally". Temporally is an adverb meaning with respect to time, or in time.

Standing waves must be in phase, inedependent of time, which means that they must have the same wavelength AND speed.