# What function or operation am I looking for?

1. Mar 10, 2012

### minio

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 $l$ and I have sine function with period length $\lambda$ originating at one end of line segment. If $l$=$\lambda$ I can easily count that there will be three points on the segment where sine value will be 0. But If $\lambda$ is slightly shorter there still will be three such points until $l=\frac{3}{2}\lambda$. Then there will be four of them. How can I describe number of such points as $f(l,\lambda)$?
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

2. Mar 11, 2012

### dodo

So, you want to know how many zeroes are in a sine wave $l/\lambda$ periods long. Which should be $\lfloor 2l/\lambda \rfloor+1$ zeroes in total, where the brackets represent the floor function.

3. Mar 11, 2012

### minio

Thank you. I never heard of floor function before. Now it is clear, that in general I was looking for floor/ceiling functions.

4. Mar 11, 2012

### dodo

You're welcome!

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