A pain wire 0.5m long has a total mass of 0.01kg and is stretched with a tension of 800N. The frequency of its fundamental note is?
Solution and answer?
Solution and answer
To find the frequency of the fundamental note of a pain wire, you can use the formula:
f = (1/2L) * sqrt(T/μ)
Where:
f is the frequency of the fundamental note,
L is the length of the wire,
T is the tension applied to the wire, and
μ is the linear mass density of the wire.
In this case, the length of the wire is 0.5m, the tension is 800N, but we still need to find the linear mass density (μ) of the wire.
Linear mass density (μ) is calculated by dividing the total mass of the wire by its length:
μ = mass / length
Given that the mass of the wire is 0.01kg and the length is 0.5m, we can calculate μ:
μ = 0.01kg / 0.5m = 0.02 kg/m
Now we can plug in the values we have into the formula to find the frequency of the fundamental note:
f = (1/2 * 0.5m) * sqrt(800N / 0.02 kg/m)
Simplifying further:
f = 1m * sqrt(40000 N * kg/m)
f = 1m * sqrt(40000 N/kg * kg/m)
f = 1m * sqrt(40000 1/s^2)
f = 1m * sqrt(40000 1/s^2)
f ≈ 200Hz
So, the frequency of the fundamental note of the pain wire is approximately 200Hz.