Traveling Wave Model: transverse wave on a string

In summary, the conversation discusses a transverse wave on a string described by a wave function, and the determination of its transverse speed and acceleration at a specific time and location. The wavelength, period, and speed of propagation of the wave are also discussed, with a hint to use the relationship k = 2\pi / \lambda to solve for the wavelength.
  • #1
mickellowery
69
0

Homework Statement


A transverse wave on a string is described by the wave function: y=(0.120m)sin([tex]\frac{\Pi}{8}[/tex]x+4[tex]\Pi[/tex]t) Determine the transverse speed and acceleration of the string at t=0.200s for the point on the string located at x=1.60m. What are the wavelength, period, and speed of propagation of this wave?


Homework Equations


vy= -[tex]\omega[/tex]Acos(kx-[tex]\omega[/tex]t)
Since f=[tex]\frac{1}{T}[/tex] and [tex]\omega[/tex] is 4[tex]\Pi[/tex] does that mean T=0.500?


The Attempt at a Solution


I was able to come up with -1.51 for the transverse speed, and I am pretty sure I understand why the acceleration is 0. I am having problems coming up with the wavelength and the proagation speed.
 
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  • #2
mickellowery said:
Since f=[tex]\frac{1}{T}[/tex] and [tex]\omega[/tex] is 4[tex]\Pi[/tex] does that mean T=0.500?
Yes.

I am having problems coming up with the wavelength and the proagation speed.
Hint: How does k relate to the wavelength?
 
  • #3
Hi Doc,

I had tried [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex] with k=frac{\Pi}{8} and it didn't work out to the right answer.
 
  • #4
What wavelength did you get?
 
  • #5
I got .0625m and the book says it should be 16m
 
  • #6
mickellowery said:
Hi Doc,

I had tried [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex] with k=frac{\Pi}{8} and it didn't work out to the right answer.
That should be k ≡ 2π/λ.
 
  • #7
So how does that change the relationship between k and [tex]\lambda[/tex]? I couldn't write it as [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex]?
 
  • #8
mickellowery said:
So how does that change the relationship between k and [tex]\lambda[/tex]? I couldn't write it as [tex]\lambda[/tex]= [tex]\frac{k}{2\Pi}[/tex]?
No. If [itex]k = 2\pi / \lambda[/itex], then [itex]\lambda = 2\pi / k[/itex]. (Just algebraic manipulation--but make sure you understand it.)
 
  • #9
Oh alright I've got it now. It's those silly little math mistakes that get me every time. Thanks much Doc.
 

1. What is the Traveling Wave Model?

The Traveling Wave Model is a mathematical model used to describe the motion of a transverse wave on a string. It takes into account the properties of the string, such as tension and density, to predict the behavior of the wave.

2. How does the Traveling Wave Model work?

The model uses the wave equation, which relates the speed, wavelength, and frequency of a wave, to calculate the displacement of the string at any given point and time. It also takes into account the boundary conditions of the string, such as fixed or free ends.

3. What are the assumptions of the Traveling Wave Model?

The model assumes that the string is perfectly flexible and has a constant tension and density along its length. It also assumes that the amplitude of the wave is small compared to the wavelength, and that the wave travels in only one direction along the string.

4. How is the Traveling Wave Model used in real life?

The Traveling Wave Model is used in various fields, such as acoustics and optics, to understand and predict the behavior of waves. It is also used in engineering to design and optimize structures, such as bridges and buildings, to withstand the effects of waves.

5. Are there any limitations to the Traveling Wave Model?

Yes, the Traveling Wave Model has some limitations. It only applies to transverse waves on a string and does not take into account the effects of other factors, such as damping and non-linear behavior. It also assumes ideal conditions, which may not always be the case in real-life situations.

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