What function or operation am I looking for?

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In summary, the conversation discusses how to mathematically describe the number of zeroes in a sine wave that is a certain length compared to its period. The formula for finding the number of zeroes is given as \lfloor 2l/\lambda \rfloor+1, where \lfloor x \rfloor is the floor function that returns the largest integer less than or equal to x. The conversation also mentions that this may be a basic concept and that the floor function may be new to the person asking the question.
  • #1
minio
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First, I am sorry for very unspecific topic, but I really have no clue what I am looking for. I need some way how in mathematical terms describe things like following:
I have line segment of length [itex]l[/itex] and I have sine function with period length [itex]\lambda[/itex] originating at one end of line segment. If [itex]l[/itex]=[itex]\lambda[/itex] I can easily count that there will be three points on the segment where sine value will be 0. But If [itex]\lambda[/itex] is slightly shorter there still will be three such points until [itex]l=\frac{3}{2}\lambda[/itex]. Then there will be four of them. How can I describe number of such points as [itex]f(l,\lambda)[/itex]?
What should I look for/study? Frankly I wouldn't be surprised if it is something really basic, because I tend to miss basic things :/ Thank you in advance
 
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  • #2
So, you want to know how many zeroes are in a sine wave [itex]l/\lambda[/itex] periods long. Which should be [itex]\lfloor 2l/\lambda \rfloor+1[/itex] zeroes in total, where the brackets represent the floor function.
 
  • #3
Thank you. I never heard of floor function before. Now it is clear, that in general I was looking for floor/ceiling functions.
 
  • #4
You're welcome!

If the ratio [itex]2l/\lambda[/itex] is positive (as it will presumably be in your case), then [itex]\lfloor 2l/\lambda \rfloor[/itex] is simply the integer part of that ratio. For example, if [itex]2l/\lambda[/itex] was 17.936, then [itex]\lfloor 2l/\lambda \rfloor[/itex] would be just 17.
 
  • #5

Based on the information provided, it seems like you are looking for a mathematical function or operation that can describe the relationship between the length of a line segment and the number of points on that segment where the sine value is 0. This could potentially be described as a function of the form f(l,\lambda) where l represents the length of the line segment and \lambda represents the period length of the sine function originating at one end of the segment.

To find this function, you may need to study trigonometry and specifically the properties and behaviors of sine functions. This will help you understand how the period length \lambda affects the number of points where the sine value is 0 on a given line segment. Additionally, studying basic algebra and functions may also be helpful in finding a way to describe this relationship mathematically.

Overall, it is important to have a strong understanding of the concepts and properties involved in order to accurately describe the relationship between these variables. I recommend consulting with a math teacher or tutor for further guidance and assistance in finding the appropriate function or operation.
 

FAQ: What function or operation am I looking for?

1. What is the purpose of a function or operation in scientific research?

A function or operation in scientific research is a mathematical or computational process that is used to analyze data, make predictions, or test hypotheses. It allows scientists to manipulate and organize data in order to gain insights and draw conclusions.

2. How do I determine which function or operation to use for my research?

The function or operation you use in your research will depend on the type of data you have, the question you are trying to answer, and the goals of your study. It is important to carefully consider your research objectives and consult with other experts in your field to determine the most appropriate function or operation for your specific study.

3. Can I use more than one function or operation in my research?

Yes, it is common for researchers to use multiple functions or operations in their research. This allows for a more comprehensive analysis of the data and can provide a more robust understanding of the research question at hand.

4. Are there any limitations or considerations when using a function or operation in scientific research?

Like any tool, functions and operations have limitations and considerations that must be taken into account. Some functions may only be appropriate for certain types of data or may have specific assumptions that must be met in order to be used effectively. It is important to thoroughly understand the function or operation you are using and its potential limitations.

5. How do I know if my results are accurate when using a function or operation?

The accuracy of your results when using a function or operation will depend on a variety of factors, including the quality of your data and the appropriateness of the function for your research question. It is important to carefully evaluate your results and consider potential sources of error or bias in your analysis.

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