Nodes and antinodes in stationary waves

In summary, when a stationary wave is formed in a string with one clamped end and one free end, a node is produced at the clamped end and an antinode is produced at the free end. This is due to the fact that the clamped end cannot move, so all the wave energy is reflected back, while the free end is not a perfect reflector and some energy can be lost. This results in a small overlap between node and antinode at the free end, rather than a true antinode. This phenomenon is also seen in wind instruments, quartz crystals, and glockenspiel bars.
  • #1
arvindsharma
21
0
Dear Friends,

in my textbook it is written that when a stationary wave is formed in a string which is clamped at one end and free at the other end then a node is produced at the clamped end and an Anti-node is produced at the free end.the explanation given is that since at clamped particle can't move so a node is formed(i am also agree with the mechanism of node formation)) and at free end since the particle can move so an anti-node is formed.my doubt is that why anti-node is formed at free end,why can't there be a situation where particle can move but does not achieve the maximum amplitude.i mean why can't there be a situation where particle at free end behaves like in-between node and Anti-node positions.please explain me the whole mechanism.

Thanks

Arvind
 
Physics news on Phys.org
  • #2
Hi and welcome to PF.
That's a good question and there are possible answers at various levels. The answer that I like best is as follows.

Firstly, let's just go over how a standing wave is formed. It's basically what happens when a wave in one direction encounters another wave (at the same frequency) from the other direction. The resulting interference gives you a stationary pattern of nodes and antinodes. The traveling wave that is approaching the clamped end cannot couple any energy to the clamp because the clamp is too massive and rigid. All the wave energy has to go somewhere and the only possible place it can go is in a 100% reflected wave, back down the string with a node at the clamp. A wave approaching the free end will actually a small amount of energy into wafting the air up and down. Most of the energy will go back from the end in the form of a reflected wave. But the free end is not, actually, a perfect reflector ; some energy can be lost to the air, so the wave at this point is not actually a perfect antinode.
You are therefore, right about not having a true antinode at the far end - good thinking.

Wind instruments have a hole / horn at the end and there is a massive 'end effect' as the energy delivered as musical sound forces a different actual frequency than would be suggested b y the physical length of the pipe. Quartz crystals, as used in oscillators, are clamped at two points, not quite at the ends, rather than right at the end because of a similar 'end effect'. Also, look at a child's glockenspiel bars, they are also mounted on nodes but there is always an overlap at each end.
 

1. What are nodes and antinodes in stationary waves?

Nodes and antinodes are specific points in a stationary wave where the amplitude of the wave is zero and maximum, respectively. In other words, nodes are points of destructive interference while antinodes are points of constructive interference.

2. How are nodes and antinodes formed in stationary waves?

Nodes and antinodes are formed due to the superposition of two waves with the same frequency and amplitude traveling in opposite directions. This results in the interference of the waves, causing certain points to have zero or maximum amplitudes.

3. How do nodes and antinodes affect the wavelength of a stationary wave?

Nodes and antinodes do not affect the wavelength of a stationary wave. The wavelength remains constant throughout the wave, but the distance between nodes and antinodes may vary depending on the frequency of the wave.

4. Can nodes and antinodes be observed in all types of waves?

Yes, nodes and antinodes can be observed in all types of waves, including sound waves, electromagnetic waves, and water waves. They are a natural phenomenon that occurs when two waves interfere with each other.

5. How do nodes and antinodes play a role in musical instruments?

Nodes and antinodes play a significant role in musical instruments, particularly in the production of different pitches. By altering the positions of nodes and antinodes, musicians can change the frequency and wavelength of the standing wave produced by the instrument, resulting in different notes or pitches.

Similar threads

  • Other Physics Topics
Replies
6
Views
1K
Replies
1
Views
2K
Replies
2
Views
1K
  • Classical Physics
Replies
7
Views
1K
  • Other Physics Topics
Replies
6
Views
3K
  • Other Physics Topics
Replies
7
Views
4K
  • Other Physics Topics
Replies
3
Views
2K
  • Classical Physics
Replies
3
Views
968
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Other Physics Topics
Replies
21
Views
5K
Back
Top