Expressing a wavelength equation in linear form; k must be determined via slope

In summary, the conversation discusses how to plot variables l and T to obtain k from the slope of a linear graph. The constants corresponding to the slope and intercept of the graph are discussed, and the equations involved are also mentioned. The need for pairs of points and the form of a straight line is also brought up.
  • #1
General_Sax
446
0

Homework Statement


How should the variables ( l and T) be plotted to obtain k from the slope of a linear graph? Identify (write out) the constants correstponding to the slope and intercept of the linear graph.

Homework Equations


l = lambda

l = (k/f)*(T/u)^0.5





The Attempt at a Solution



k^2 = [ (f^2)*(u) ] * [ (l^2)/T ]

(l^2)/T = x

(f^2)* u = m

K^2 = mx + 0

b = 0
 
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  • #2
For a plot you need pairs of points (x, y). So what are you going to plot on the x-axis and what on the y-axis? A straight line is of the form y = mx + b. What is your y? It can't be k2 because you don't know what it is.
 
  • #3
lol, good point. I'll get back to you.
 

Related to Expressing a wavelength equation in linear form; k must be determined via slope

1) What is the purpose of expressing a wavelength equation in linear form?

Expressing a wavelength equation in linear form allows for a more simplified and easier-to-understand representation of the relationship between wavelength and other variables. It also allows for easier calculation and manipulation of the equation.

2) How is the value of k determined via slope?

The value of k in a linear wavelength equation is determined by finding the slope of the line created by plotting wavelength on the y-axis and the other variable on the x-axis. The slope represents the change in wavelength for each unit change in the other variable, and this value is equivalent to k in the linear form of the equation.

3) Can k be determined through experimental data?

Yes, the value of k can be determined through experimental data by plotting the data points and finding the slope of the resulting line. This value can then be used in the linear wavelength equation.

4) What are the assumptions made when expressing a wavelength equation in linear form?

The main assumption is that the relationship between wavelength and the other variable is linear. This means that the change in wavelength is proportional to the change in the other variable, and the slope of the line remains constant.

5) Can a linear wavelength equation accurately represent all types of relationships between wavelength and other variables?

No, a linear wavelength equation can only accurately represent relationships that are linear. If the relationship is nonlinear, a linear equation will not accurately represent the relationship and may lead to incorrect predictions or calculations.

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