Standing waves and phase difference

Can someone please explain to me how standing waves work as well as phase difference. Thank you.

Standing waves are formed when a progressive wave reflects off of a boundary and superposes with the incident wave to form a resultant wave with nodes and antinodes. Nodes are points along the stationary wave where the amplitude is 0 due to destructive interference whereas antinodes are points along the wave where the amplitude is at a maximum due to constructive interference.

Phase difference is essentially how far through the wave cycle one wave/point along a wave is in comparison to another wave/point along the same wave. Those that are in phase (have a phase difference of 0°/0 rads) are at exactly the same point in the wave cycle, that is, they both have the exact same displacement as one another. Those that are in antiphase (have a phase difference of 180°/pi rads) and so when one point has maximum displacement, another has minimum displacement. For waves/points along a wave that have a phase difference of 90° or pi/2 rads) when one point has 0 displacement the other has a maximum displacement.

Hopefully this helps.

Reply 2

Jennifer50

Can you please explain this to me:

I think it's called the 1st harmonic and I read that there is a second and third as well.

Reply 3

Jpw1097

Original post by Jennifer50

Can you please explain this to me:

I think it's called the 1st harmonic and I read that there is a second and third as well.

The first harmonic is also known as the fundamental frequency, it is the lowest frequency possible for that particular wave with a given wavelength. The second harmonic has a frequency twice that of the first harmonic. Suppose the first harmonic or fundamental frequency is 50Hz, the second harmonic would have a frequency of 100Hz, the third 150Hz, and so on.

Reply 4

Kallisto

Entertainment Forum Helper

Original post by Jpw1097

Nice, very nice. Good explanation, really. But in terms of explaining how standing waves work, there is an aspect which you may mention, namely that the standing waves are vibrating because of incident wave and reflective wave come upon.

(edited 8 years ago)

Reply 5

derpz

Original post by Jennifer50

Can someone please explain to me how standing waves work as well as phase difference. Thank you.

I answered a question about standing waves earlier, so here's my explanation which is mostly a comparison with progressive waves:

Progressive waves are longitudinal or transverse waves which basically transfer energy from one point to another. For example any wave out of the electromagnetic spectrum is progressive (e.g. visible light transfers energy in the form of light).

Standing waves on the otherhand trap energy between two points. You also need to know how they are formed:

Progressive waves are initially formed, which would travel in opposite directions, and then be reflected off whatever is keeping the medium together and when they reflect back, they interfere and form "nodes" and "antinodes".

This might make it easier to understand:

Here, the vibrator would have a certain frequency, which would first form a progressvie wave. This wave would then be reflected off the pulley and the vibrator as it travels along the string. It then interferes constructively and destructively.

This is where "nodes" and "antinodes" come in.

Constructive interference = Antinode forms
Destructive interference = Node forms

A node is the minimum aplitude on a standing wave. Here, it would be the points where it seems like the string interceps, as the amplitude is zero.

An antinode is where the amplitude is maximum, which is the centre of the oval like shape formed, from the bottom to the very top.

If that doesnt really make sense, this should:

Also, a key difference is to remember that a standing wave has many amplitudes, whereas a progressive wave has only 1 amplitude which would be the max point. For example, on the standing wave any point between a node and antidnode is an amplitude but on a progressive wave these would just be points on the wave which have displacements.

Here's a comparison between the two:

Phase difference:
"The angle by which a wave lags or leads another"

Bascially, full wavelength has a phase difference of zero degrees (or 360 degrees) so it forms a full circle.

Try to remember that its all measured in angles relative to 360 degrees which is one full wavelength. So for example half a wvelength has a phase differnece of half of 360; 2 wavelengths would have a phase difference of two times 360...

Another thing to learn it the term "antiphase" which is when a trough and peak of two waves line up, e.g.:

On the left we see that two waves in phase (phase difference which is any amount of full wavlengths e.g. 360, 720 degrees) forms 1 wave which has a greater amplitude when they interfere which results in constructive interference.

On the right you can see that two waves which are in antiphase interfere destrucivel and from a wave with basically no amplitude.

I know my explanation is kind of hard to understand, but if you dont understand any points or have any other questions just let me know

Reply 6

Kallisto

Entertainment Forum Helper

Original post by derpz

(...)
A node is the minimum amplitude on a standing wave. Here, it would be the points where it seems like the string interceps, as the amplitude is zero.
(...)

Sorry that I am nagging a bit about your explanation, but an amplitude is defined as the maximum point of a sinus curve, never as the minimum one.

Reply 7

derpz

Original post by Kallisto

Sorry that I am nagging a bit about your explanation, but an amplitude is defined as the maximum point of a sinus curve, never as the minimum one.

The definition that I've been taught is:

"The maximum displacement from the undistrubed position", and in a progressive wave, there is only 1 point of maximum displacement (the peak/trough which have the same value just that one is negative).

I think I may have accidentaly written "minimum", but I definately meant maximum.

Thanks for correcting me there :smile:

Reply 8

Kallisto

Entertainment Forum Helper

Original post by derpz

(...)
I think I may have accidentaly written "minimum", but I definately meant maximum.

Thanks for correcting me there :smile:

Fair enough. The rest of the explanation of yours is okay, but I must admit that I have never heard of an experiment set-up with a pulley, mass and vibrator when I was taught in standing waves.

(edited 8 years ago)

Reply 9

derpz

Original post by Kallisto

Fair enough. The rest of the explanation of yours is okay, but I must admit that I have never heard of an experiment set-up with a pulley, mass and vibrator when I was teached in standing waves.

I think as long as you know that you need a source to initiate the wave and two places where they reflect and you can identify these in an exam question you should be fine, dont really need to know specifics.

Reply 10

Kyx

Original post by Kallisto

Fair enough. The rest of the explanation of yours is okay, but I must admit that I have never heard of an experiment set-up with a pulley, mass and vibrator when I was teached in standing waves.

*taught