Question

A violin string vibrates at 260 Hz when unfingered. At what frequency will it vibrate if it is fingered one fourth of the way down from the end

Answer 1

346.66 Hz

Step-by-step explanation:

`l_1` = Length of string which is unfingered = l

`l_2` = Length of string which is vibrate when fingered =
`l-(1)/(4)l=(3)/(4)l`

`f_1` = Unfingered frequency = 260 Hz

`f_2` = Fingered frequency

Frequency is inversely proportional to length

`f=(1)/(l)`

So,

`(f_1)/(f_2)=(l_2)/(l_1)\\\Rightarrow (f_1)/(f_2)=((3)/(4)l)/(l)\\\Rightarrow (f_1)/(f_2)=(3)/(4)\\\Rightarrow f_2=(4)/(3)f_1\\\Rightarrow f_2=(4)/(3)260\\\Rightarrow f_2=346.66\ Hz`

The frequency of the fingered string is 346.66 Hz