What is the fundamental frequency if the tension in the string is halved?

0.25 L (√ (T/2μ)

Explanation:

Process

Let's say we have the following data set:

f = f₁

and let's assume that the length of the string is halved, which gives L₁ = 0.5 L

Suppose the tension is halved, so the tension is 0.5 T

Substituting in Fn = (n/2L) * (√T/μ)

= (1/2*0.5L) (√0.5*T/μ)

= 0.25 L (√ (T/2μ)

In general, v/2 = 0.25 L (√ (T/2μ)

v = 0.5 L (√ (T/2μ)

As we can see, the tension is always being halved.