Question

The frequency of vibration (f) of a string varies directly as the square root of the tension (T) and inversely as the length (L) of the string. If the frequency is 60 vibrations per second with the tension is 121 lb and the length of the string is 12 feet, find the frequency with the tension is 81 lb and the string is 9 feet.

Answer 1

`f = (720)/(11)`

Explanation:

Given

`f\ \alpha\ (\sqrt T)/(L)` --- The variation

`f = 60; T = 121; L = 12`

Required

Find f, when T =81; L = 9

We have:

`f\ \alpha\ (\sqrt T)/(L)`

Express as equation

`f = k(\sqrt T)/(L)`

Make k the subject

`k = (fL)/(\sqrt T)`

When
`f = 60; T = 121; L = 12`

`k = \frac{60 * 12}{\sqrt {121}}`

`k = (60 * 12)/(11)`

`k = (720)/(11)`

To solve for f, when T =81; L = 9

We have:

`f = k(\sqrt T)/(L)`

`f = (720)/(11) * (√(81))/(9)`

`f = (720)/(11) * (9)/(9)`

`f = (720)/(11) * 1`

`f = (720)/(11)`