Analyzing a Wave: Homework Solutions

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In summary, the conversation discusses a problem involving finding the tension of a string and its relationship to wave velocity. The conversation covers various equations and solutions, including calculating the maximum displacement and using v=ω/k to find the speed. The group also discusses the possibility of the question asking for lateral velocity instead of wave velocity and the importance of consistent units when solving the problem.
  • #1
aliaze1
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Homework Statement



http://photo.ringo.com/230/230997145O975467146.jpg [Broken]

http://photo.ringo.com/230/230997145O975467146.jpg [Broken]

Homework Equations



λ=v/f
k=2π/λ
ω=2πf
T=1/f
v=ω/k
V(string) = √(Tension of string/μ), where μ = denisty

D(x,t) = A sin (kx - ωt + Φ)

The Attempt at a Solution



I found the maximum displacement as 2, found from the given equation

The third part seemed to be the next simplest, so using v=ω/k, I calculated 638/12.57 as the speed, which was incorrect

To my knowledge, this speed is needed to calculate the tension of part 1
 
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  • #3
i guess it is possible, but that is the exact question copied word-for-word
 
  • #4
what does d(D(x,y))/dt means?
 
  • #5
I just realized that the third part is not required to complete the first part,

using v=ω/k, and plugging this v into

V(string) = √(Tension of string/μ), where μ = denisty;

I get an answer of 12880.7, which is essentially 12.9 *103...the answer however is simply 12.9...

where am i going wrong?

thanks
 
  • #6
I thought it had to do with the amplitude being in centimeters, so I divided by 100, but that still is 129 not 12.9...
 
  • #7
Make sure all units are consistent. The linear mass density is 5 g/ m as opposed to 0.05 g /cm or 0.005 kg/m. Perhaps that is where one is off by 3 or 1 order of magnitude depending on the values one uses. Tension should be in Newtons (for SI/mks).
 
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  • #8
Astronuc said:
Make sure all units are consistent. The linear mass density is 5 g/ m as opposed to 0.05 g /cm or 0.005 kg/m. Perhaps that is where one is off by 3 or 1 order of magnitude depending on the values one uses. Tension should be in Newtons (for SI/mks).

thanks!, makes sense
 

1. What is the purpose of analyzing a wave?

The purpose of analyzing a wave is to understand its properties and behavior in order to make predictions and draw conclusions about the phenomena it represents. This can help in various scientific fields, such as physics, engineering, and meteorology.

2. What are some common methods used to analyze a wave?

There are several common methods used to analyze a wave, including Fourier analysis, spectral analysis, and wavelet analysis. These methods involve breaking down a wave into its component parts and studying the characteristics of each part.

3. How do you determine the amplitude of a wave?

The amplitude of a wave is determined by measuring the distance between the equilibrium point (the middle of the wave) and the highest or lowest point of the wave. This distance represents the maximum displacement of the wave from its equilibrium position.

4. What is the relationship between wavelength and frequency?

The wavelength and frequency of a wave are inversely proportional. This means that as the wavelength increases, the frequency decreases, and vice versa. This relationship is described by the formula: wavelength = speed of the wave / frequency.

5. Can different types of waves be analyzed using the same methods?

Yes, many of the methods used to analyze waves can be applied to different types of waves, such as sound waves, electromagnetic waves, and water waves. However, some methods may be more suitable for certain types of waves depending on their properties and characteristics.

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