Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:
Where <em>k</em> is the constant of variation.
Inverse variation is in the form:
In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using <em>f</em> for frequency and <em>l</em> for length:
We can solve for the constant of variation. We know that the frequency <em>f</em> is 4.3 when the length is 0.65 meters long. Thus:
Solve for <em>k: </em>
<em /><em />
<em />
So, our equation becomes:
Then when the length is 0.5 meters, the frequency will be: