Mathematica Representation of a wave

In summary, a sinusoidal wave propagates along a stretched string with a period of 0.04 seconds and an amplitude of 4mm. The points at x=0 and x=0.0900m are within one wavelength of each other, and using the formula y(x,t)=Acos(2pi(x/lambda-t/T)), the wavelength is found to be 0.14m. By considering the distance between two waves and dividing it by time, the wave speed can be easily calculated.
  • #1
ku1005
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0

Homework Statement



"A sinusoidal wave is propagating along a stretched stringas a function of time is graphed in the figure (attached) for particles at x = 0 and x =0.0900m. a) what is the period of the wave ( my ans = 0.04 sec

b) what is the amplitude of the wave ( my ans = 4mm)

c)you are told that the 2 points x=0 and x=0.0900m are within one wavelength of each other. If the wave is moving in the +x direction, determine the wavelenght and the wave speed."





Homework Equations



y(x ,t) = A cos(2pi ( x/lambda - t/T))

ie the mathematical representation of a wave

The Attempt at a Solution



I have already posted this Q previously, but fear that how I posted it made it seem unsolvable, this is what I did again:

0.75 = cos (2pi (0.09/lambda - 0 )) where I get lambda, and thus wavelength to equal 0.78... which isn't correct since the answer is something like 0.14m

any pointers on how to solve would be great!
 

Attachments

  • wave figure.jpg
    wave figure.jpg
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  • #2
I can't open your attachment as yet (its still pending approval) but I'll assume you took the period and amplitude from information of the graphs.

Do the two graphs should show a phase difference? If they do, you can easily use this to establish how long the wave takes to get from the first point to the second. Youve then got a distance and a time from which a speed is easy.
 
  • #3
yeah i got it now...u use the distance travelled...ie between 2 waves...so from say a peak to the next peak ...adn diide by time...makes it REAL simple when you consider this way...cheers for the attempt...no1 else seemed to b able to get it?
 

What is a Mathematica representation of a wave?

A Mathematica representation of a wave is a mathematical expression or function that describes the behavior of a wave, such as its amplitude, frequency, and wavelength. It is often used to model physical phenomena, such as sound and light waves.

How is a wave represented in Mathematica?

A wave can be represented in Mathematica using various functions, such as Sin, Cos, and Exp. These functions can be combined to create a more complex representation that accurately describes the behavior of the wave.

What are the advantages of using Mathematica for wave representation?

Mathematica has powerful mathematical and computational capabilities that make it well-suited for representing complex waves. It also has a user-friendly interface and a vast library of built-in functions that can be used to manipulate and analyze the wave representation.

Can Mathematica represent all types of waves?

Yes, Mathematica can represent a wide range of waves, including electromagnetic waves, sound waves, and water waves. It can also handle both one-dimensional and two-dimensional wave representations.

Is Mathematica representation of a wave accurate?

Yes, the accuracy of a Mathematica representation of a wave depends on the accuracy of the input parameters and the complexity of the wave function. With proper input and careful manipulation, Mathematica can produce highly accurate representations of waves.

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