Understanding Standing Waves: Clarity on Conditions

In summary, standing waves are created by the combination of reflection and interference, resulting in characteristic patterns of vibration. The conditions for constructive interference include the waves having the same frequency and velocity, and changing phase upon reflection from a fixed end. The waves do not need to have the same amplitude, but must be in phase temporally. Standing waves can be produced by the interference of two waves of the same frequency moving in opposite directions, as long as they maintain the same initial phase difference.
  • #1
Amith2006
427
2
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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  • #2
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.
 
  • #3
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?
 
Last edited:
  • #4
This java applet could be of some help too.

http://www.walter-fendt.de/ph14e/stwaverefl.htm
 
  • #5
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.
 

1. What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This creates a pattern where certain points, called nodes, do not experience any displacement while other points, called antinodes, experience maximum displacement.

2. How do standing waves form?

Standing waves form when there is a fixed boundary or a boundary with a large difference in impedance. This can occur in various systems such as strings, pipes, and membranes. When a wave is reflected off of the boundary and interferes with the incoming wave, it creates the pattern of standing waves.

3. What are the conditions for standing waves to occur?

There are two main conditions for standing waves to occur. The first is that there must be two waves with the same frequency and amplitude traveling in opposite directions. The second is that there must be a fixed or reflective boundary present. If these conditions are met, standing waves will form.

4. What is the relationship between wavelength and the length of the medium for standing waves?

The length of the medium must be a multiple of half the wavelength of the wave for standing waves to occur. This means that the number of half wavelengths that fit in the medium must be a whole number, such as 1, 2, 3, etc. This is known as the resonance condition and is necessary for the standing wave pattern to form.

5. What are some real-world applications of standing waves?

One common application of standing waves is in musical instruments. For example, the strings on a guitar or the air column in a flute will create standing waves when plucked or blown into, producing different pitches. Standing waves also play a role in the design of acoustic spaces, such as concert halls, to ensure good sound quality and resonance. Additionally, standing waves are used in medical imaging techniques, such as ultrasound, to produce images of internal structures in the body.

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