Question

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.

Answer 1

Hmmm. Make a table of Length^.5 *freq
.46*sqrt100=4.6
.52*sqrt80= 4.65
1.01*sqrt20=4.51
Try the rest.

Answer 2

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.

Answer 3

I would graph freqency vs 1/SQRT(length)

Answer 4

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.