Question

Could someone please help me? Thank you and explain the work because I don’t get this

Answer 1

5.59 times per second.

Explanation:

Direct variation is in the form:

`y=kx`

Where k is the constant of variation.

Inverse variation is in the form:

`\displaystyle y=(k)/(x)`

In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using f for frequency and l for length:

`\displaystyle f=(k)/(\ell)`

We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:

`\displaystyle 4.3=(k)/(0.65)`

Solve for k:

`k=4.3(0.65)=2.795`

So, our equation becomes:

`\displaystyle f=(2.795)/(\ell)`

Then when the length is 0.5 meters, the frequency will be:

`\displaystyle f=(2.795)/(.5)=5.59\text{ times per second.}`