Understanding Standing Waves: Clarity on Conditions

AI Thread Summary
Standing waves are produced through the interference of two waves that have the same frequency and wavelength, and they must be in phase temporally for constructive interference. While the amplitudes of the waves do not need to be the same, the waves must travel at the same velocity. The phenomenon occurs due to reflection and interference, particularly in fixed-end scenarios where waves change phase upon reflection. It is clarified that standing waves can also result from two waves of the same frequency moving in opposite directions, even if there is a constant phase difference, but this phase difference will not remain constant over time. Understanding these conditions is essential for grasping the concept of standing waves in various physical contexts.
Amith2006
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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.
 
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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.
 
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?
 
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This java applet could be of some help too.

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

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