Using the data below, suggest a proportionality statement.
Length (cm) Frequency (Hz)
100 0.46
80 0.52
60 0.62
40 0.74
20 1.01
I think it's f ¡Ø 1/¡Ìlength (one over square root of length)
or is it l ¡Ø 1/f^2
By the way, the length is the controlled variable.
Hmmm. Make a table of Length^.5 *freq
.46*sqrt100=4.6
.52*sqrt80= 4.65
1.01*sqrt20=4.51
Try the rest.
They all have values around there, so I'm sure the proportionality is something like that. But I'm supposed to graph it to show this proportionality and I'm not sure what goes on the axis.
Is the y-axis f and x-axis 1/length^0.5
or is the y-axis 1/f^2 and x-axis length
It's the same proportionality, just a bit different.
I would graph freqency vs 1/SQRT(length)
I would graph frequency^2 versus 1/length
alternatively, graph log frequency versus log length
then if y = k/x^2
log y = log k - log x^2
which is
log y = log k - 2 log x
If you have log graph paper this works particularly easily, the intercept being k and the slope in this case being -2
(if we had not guessed the power 2, the slope would have given us the power.
To determine the proportionality statement, we need to examine the relationship between the length (cm) and frequency (Hz) by looking at the given data.
One way to find the proportionality pattern is by assessing how one variable changes relative to the other. In this case, we have a controlled variable (length) and a responding variable (frequency). To understand the relationship, let's consider the given data:
Length (cm) Frequency (Hz)
100 0.46
80 0.52
60 0.62
40 0.74
20 1.01
If we observe the data closely, we can see that as the length decreases, the frequency tends to increase. Additionally, we can observe that the change in frequency is not directly proportional to the reciprocal of the length or the square of the frequency.
To find the appropriate proportionality statement, we should investigate how the variables relate to each other. One way to do this is by plotting the data points on a graph and examining the resulting trendline. By plotting the length on the x-axis and the frequency on the y-axis, we can generate a scatter plot.
After plotting the data, we can draw a line of best fit through the points to reveal the overall trend. The equation of that line can then be used to identify the proportionality statement.
While I cannot create visual representations, I recommend plotting the data on a graph and drawing the line of best fit. Once you have done that, you can determine the equation of the line (y = mx + b, where y represents the frequency and x represents the length). The resulting equation will provide the desired proportionality statement.
Based on the data provided, plotting the points and finding the line of best fit will help you determine the proportionality statement accurately.