The frequency of a note produced by a vibrating wire depends on various factors, including the length of the wire and the tension applied to it. We can use the formula for the fundamental frequency of a vibrating wire:
f = (1/2L) * sqrt(T/μ) ,
Where:
f = frequency
L = length of the wire
T = tension applied to the wire
μ = linear mass density of the wire
Let's calculate the initial linear mass density (μ) using the given information:
Length (L) = 80 cm = 0.8 m
Tension (T) = 40 N
Next, we'll find the initial frequency (f1) using the formula:
f1 = (1/2L) * sqrt(T/μ)
Now, we'll calculate the new length and tension:
New Length (L2) = 0.8 m / 2 = 0.4 m (halved)
New Tension (T2) = 40 N * 2 = 80 N (doubled)
Finally, we can find the new frequency (f2) using the same formula:
f2 = (1/2L2) * sqrt(T2/μ)
Comparing the initial frequency (f1) and the new frequency (f2) will allow us to determine the change in frequency.