Question

The fundamental frequency of a guitar string is 367 hz . part a what is the fundamental frequency if the tension in the string is halved?

Answer 1

The fundamental frequency of a string is given by:

`f_1 = (1)/(2L) \sqrt{ (T)/(\mu) }`
where L is the string's length, T the tension and
`\mu` the linear density of the string.

We can see that f1 is proportional to the square root of T:
`√(T)`.
This means that if the new tension is half the initial value, the new fundamental frequency will be proportional to
`\sqrt{ (T)/(2) }= ( √(T) )/( √(2) )= (f_1)/( √(2) )`

So, the new fundamental frequency will be

`f_1 ' = (367 Hz)/( √(2) )=259.5 Hz`