Algebra 1 Honors

Question

The length of a piano string varies indirectly with the frequency of vibrations of the string. When the length is 2.5 feet, the frequency is 2 Hz. What is the frequency of a string 2 feet long?

Answer 1

l = length

f = frequency

k = constant of variation

l = f/k (length varies indirectly with frequency)

Given when l = 2.5, that f =2, so can determine k:

2.5 = 2/k

k = 0.8

constant of variation is 0.8, so relationship can be written as:

l = f/0.8

l = 1.25f

when l = 2

2 = 1.25f

1.6 = f

Answer 2

This problem can be looked at somewhat like a conversion problem and therefore, can be done one of two ways. The first way is likely how your teacher taught you to solve it, which is to set up two fractions that equal each other. In away, set up a ratio.

(x₁÷y₁)=(x₂÷y₂₎

After you set it up as two fractions equal to one another, then you will have one unknown. you can then multiply the denominator to isolate the unknown--think rearrange to get the unknown. I would take the two given and put them in a ratio to each other. The length, which you are given two of, should be either both the y variables or the x variables.

So,

(2Hz÷2.5ft)=(xHz÷2ft)

x=1.6Hz