What is the rate of change of amplitude for standing waves with respect to x?

Click For Summary

Discussion Overview

The discussion revolves around the differentiation of the equation for standing waves, specifically focusing on the rate of change of amplitude with respect to the position variable "x". Participants explore the implications of differentiating the wave equation and the meaning of the results at a specific time.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents the standing wave equation, y=Asinkxcosωt, and questions what the differentiation with respect to "x" yields, particularly at t=0.
  • Another participant states that differentiating with respect to "x" provides the slope of the wave at a given instant, indicating a relationship to the wave's shape.
  • A different viewpoint suggests that the rate of change of amplitude is related to the velocity of the particle, expressed as dy/dt.
  • One participant discusses the scenario of a string oscillating at its fundamental frequency, suggesting that differentiating the equation y=Asinkx at t=0 gives a snapshot of the wave and leads to a specific expression for the rate of change of amplitude.
  • Another participant reiterates the idea that the rate of change of amplitude is velocity and expresses a desire to quantify how amplitude changes as one moves along the x-axis.
  • A later reply affirms the previous statement about measuring amplitude changes along the x-axis.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the differentiation results and the relationship between amplitude change and velocity. The discussion remains unresolved with multiple competing interpretations present.

Contextual Notes

Participants do not clarify the assumptions underlying their interpretations of the wave equation or the conditions under which their statements hold true.

Who May Find This Useful

Individuals interested in wave mechanics, particularly those studying standing waves and their mathematical representations, may find this discussion relevant.

nil1996
Messages
301
Reaction score
7
Equation of standing waves→ y=Asinkxcosωt

What do i get if i differentiate the above equation with respect to "x" ?
Do i get the rate of change of amplitude when i put t=0?
 
Physics news on Phys.org
when you differentiate it with respect to x, then you get slope of the curve/wave at a given instant ##\frac{dy}{dx}=slope##.
 
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle
 
Lets consider a string oscillating in fundamental frequency. In the wave equation if i put t=0 the i will get a snapshot of the wave in which all particles will be at their amplitudes. Now if i differentiate the equation that is y=Asinkx i will get something like [itex]\frac{dy}{dx}[/itex]=Akcoskx and i think this will be the rate of change of amplitude on the string. Isn't it right?
 
NihalSh said:
rate of change of amplitude is velocity, ##\frac{dy}{dt}=##velocity of particle

I want to say how much the amplitude changes as i move forward on x-axis.
 
nil1996 said:
I want to say how much the amplitude changes as i move forward on x-axis.

Yes, you can say that!
 

Similar threads

Undergrad Will Increasing Tension of a Two Loop Standing Wave Change its Frequency?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Standing Waves by Reflection: Losses of the Reflected Wave
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Mechanism of Energy Conservation in Zero-Amplitude Sum of EM Waveforms
  • · Replies 21 ·
Replies
21
Views
3K
Graduate Amplitude of a stationary wave
  • · Replies 3 ·
Replies
3
Views
2K
High School Solving Confusion with Waves in Physics
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Solution to the 1D wave equation for a finite length plane wave tube
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Edge of Brillouin zone,1D crystal, graphene, standing wave, band gap
  • · Replies 2 ·
Replies
2
Views
2K
Agree or Disagree? Analyzing Wave Amplitudes
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How exactly are standing waves formed?
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad ΔAmplitude of wave on rope with a change in linear density
  • · Replies 3 ·
Replies
3
Views
2K