How is equation 15.14 derived in the wave speed derivation?

Click For Summary

Homework Help Overview

The discussion revolves around the derivation of equation 15.14 in the context of wave speed, specifically focusing on the underlying principles and assumptions involved in the derivation process.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the derivation by considering small angle approximations but expresses difficulty in connecting this to equation 15.14. Other participants emphasize the need to clarify the origin of the equation rather than its meaning.

Discussion Status

The discussion is ongoing, with participants exploring the conceptual basis of the equation and questioning the assumptions related to the tension in the rope. There is no explicit consensus on the derivation yet, but the dialogue indicates a productive inquiry into the foundational aspects of the equation.

Contextual Notes

Participants are grappling with the implications of the tension in the rope and its relationship to the slope, which may be influencing their understanding of the derivation.

Fluxthroughme
Messages
71
Reaction score
0
33tt7og.png
With reference to this diagram, my textbook tells me the following:


312cn5v.png


I am able to follow the rest of the derivation after this point, but I do not understand where equation 15.14 came from? I'm trying to think in terms of small angle approximations, but nothing is really coming of that. Any help is appreciated.

Thanks.
 
Physics news on Phys.org
The equation just says mathematically what the words say.
 
tms said:
The equation just says mathematically what the words say.

I know what the equation says. I don't know where it came from, I.E, I don't know why it is true.
 
The rope can only experience tension. Therefore, the slope of the rope at any point must also coincide with the direction of the tension force in the rope.
 

Similar threads

Replies
8
Views
1K
  • · Replies 1 ·
Replies
1
Views
934
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
8
Views
2K