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### Course: Oscillations and waves (Essentials) - Class 11th>Unit 3

Lesson 6: Why empty bottles can be used to make music!

# Standing waves on strings

A standing wave occurs when two waves of the same frequency and amplitude are moving in opposite directions and interfere with each other. It has certain points (called nodes) where the amplitude is always zero, and other points (called antinodes) where the amplitude fluctuates with maximum intensity. Use the distance between two consecutive nodes or two consecutive antinodes to calculate the length of a standing wave. Created by David SantoPietro.

## Want to join the conversation?

• At , he says the two waves are lining up constructively. But if one is above and one is below the equilibrium point, wouldn't they cancel out?

I'm confused too as to whether we are actually talking about two waves overlapping, or one wave that has gone to the right and then to the left. He said the latter but then why are we talking about interference if it's just one wave?
• think about it, he said (more or less) that we're continuously forming disturbances(after talking about pulses),
so, after the first reflection, don't you think at a given instance of time at any point there will be (at least) two simultaneous waves == interference?
As we've defined standing waves to not move right or left (along axis/eq. line), don't you think these points must coincide exactly as they had before to form that exact possible wavelength?
So after the first reflection, the no. of reflections really doesn't matter as they're coinciding at the exact place, further, the ind. waves are moving, so their regions of 'activity'/'disturbances' (except nodes....imagine!it's fun ;}) are changing, so their shifting vertically (here) down and then back up...you know...oscillate! They oscillate up and down! (maybe the flat-line is when they have a complete pi shift overlap= total destructive interference)
[and besides, do we assume the wave to be finite(that is not directly from its source?---> an actual question, not a rhetorical device;)]

at least this is how I've imagined (notice the bold font) it and I'm no professional, if wrong do correct me,
Hope this helps!
Onward!
• at why does the pulse turns upside down after reflection?
• on reflection, there is a change in phase. (If the medium is fixed... if it is free to move, then there is no phase change)
• What's the difference between a crest and an antinode?
• A crest is a point where height of the wave is equivalent to its amplitude (the highest points on the wave). An antinode is the area that moves the most in a standing wave. Note that all waves have a crest, but not all waves have antinodes.
• At , isn't the wavelength of the third harmonic suppose to be 3/2 not 2/3? there's 1 wavelength + 1/2 wavelength
• You're correct that for the third harmonic there are 3/2 waves on the string. However the wavelength is only 2/3 of that string. And in this example the string is 10 meters. Thus the wavelength is (2/3)*10 m.

I'm guessing that you're mixing up the wavelength with the number of waves in this case.
• From what I know, waves are the transfer of energy in the form of a disturbance ( vibration in particles of a medium). If nodes are places where the "string" or any medium does not oscillate does that mean that energy is not transferred at those points of destructive interference?
• Actually what does harmonics mean?
• The "harmonics" are exactly the "standing waves" that this video is about. The "first harmonic" is the same as the "fundamental" wave that he discusses in the first part of the video. Its wavelength is twice the length of the string.

At in the video, he introduces the "second harmonic", which has a node in the center, and its wavelength is equal to the length of the string. The frequencies of the higher harmonics get higher and higher as the wavelengths get shorter and shorter.
• Can you create travelling waves in a medium that has boundaries?
• when we say n is the number of harmonics, what do we mean by a harmonic?
• a 'harmonic' refers to a probable part of a simple harmonic wave which can be found in the oscillation of a standing wave
(1 vote)
• I'm really confused that why doesn't standing waves form in case of destructive interference ( when waves completely cancel each other) or I can ask that why does standing waves form even? Why don't they just cancel out each other as in case of destructive interference? Is standing waves phenomena restricted to wave and it's reflection? I'm really confused
• at , why do we get destructive interference? Both the reflected and the incoming waves are at 0 amplitudes, so they don't even have values to cancel each other to begin with. And why would the antinodes be points of constructive interference? Don't the incoming and reflected have opposite amplitudes, so shouldn't they cancel each other out?