Are nodes on a string perfect nulls?

In summary, the conversation discusses the concept of energy loss in standing waves and how it affects the amplitude and null points. It is explained that there is no such thing as a perfect null in real life due to energy losses throughout the string, not just at the point of reflection. The example is given of a situation where 100% of the wave is transmitted at the end, resulting in no reflection and no nodes. The conversation also touches on the idea of ideal strings and how energy loss at the reflection point would be equivalent to transmission. It is clarified that the traditional treatment of 100% reflection at the ends of a string only applies to traveling waves, not standing waves. In conclusion, the conversation highlights the importance of considering energy loss when
  • #1
musichascolors
21
2
Maybe I'm thinking about this incorrectly, but I would assume that the wave loses energy after bouncing back and before hitting the wave moving in the opposite direction. Wouldn't this prevent a perfect null (if the amplitudes were different)?
 
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  • #2
Welcome to PF;
The short answer is "no" - there is no such thing as perfection in real life.
You are correct - energy losses, which occur throughout the string, not just at reflection, mean that the relations you learn for standing waves are only approximate.
You can imagine the situation where 100% of the wave gets transmitted at the end - in which case there is no reflection, and thus no cancellation, and so there are no nodes at all.
 
  • #3
Simon Bridge said:
You can imagine the situation where 100% of the wave gets transmitted at the end - in which case there is no reflection, and thus no cancellation, and so there are no nodes at all.

Thanks, could you please rephrase this? No sure what you mean.
 
  • #4
In your discussion post #1 you imagined some energy loss after reflection - instead, imagine the energy loss occurring at the point of reflection: then we can keep ideal strings in between the reflection points.
Loss of energy at the reflection point would be equivalent to having some transmittion (along an ideal string) at that point.

The usual treatment has 100% reflection at the ends of the string of a traveling wave amplitude A - this would be the same as 0% energy loss at each reflection.
The result is a standing wave with 0 amplitude at the nodes and amplitude 2A at the antinodes.

Imagine there were 100% energy loss at the ends. Then there would be 0% reflection ... it's the same wavelength so the theoretical nodes and antinodes are in the same place, but there can be no standing wave without the reflected wave ... so, logically, what is the amplitude of the motion at the node and antinode locations?
 
  • #5
Yes, I understand that their is energy loss both before, during, and after the reflection. Thank you for clarifying that null points aren't "perfect nulls" which makes sense.
 

Related to Are nodes on a string perfect nulls?

1. What are nodes on a string?

Nodes on a string refer to the points where the string is attached or fixed, creating a stable structure. They can be physical objects or theoretical points in a mathematical model.

2. What is a perfect null in the context of nodes on a string?

In the context of nodes on a string, a perfect null refers to a node that does not vibrate or move when the string is plucked or disturbed. It is essentially a point of no vibration, creating a stable and balanced structure.

3. Are all nodes on a string perfect nulls?

No, not all nodes on a string are perfect nulls. In fact, in most cases, only a few specific nodes on a string will be perfect nulls, while the others will vibrate and move in response to disturbances.

4. How do you determine which nodes on a string are perfect nulls?

The placement of perfect nulls on a string depends on the length and tension of the string. Generally, the nodes that are located at points that are fractions of the string's length (such as 1/2, 1/3, 1/4, etc.) will be perfect nulls. This can be calculated using mathematical equations or through experimentation.

5. What is the significance of perfect nulls in the study of waves and vibrations?

Perfect nulls play an important role in understanding the behavior of waves and vibrations. They help us identify and analyze the different modes of vibration that can occur in a system, and provide a basis for understanding complex wave patterns. Additionally, the concept of perfect nulls is fundamental in the study of musical instruments and acoustics.

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