A 38 cm length of wire has a mass of 6.0 g. It is stretched between two fixed supports and is under a tension of 145 N. What is the fundamental frequency of this wire?
To find the fundamental frequency of a wire, we need to use the formula:
f = (1 / 2L) * √(T / μ)
Where:
f = fundamental frequency
L = length of the wire
T = tension in the wire
μ = linear mass density of the wire (mass per unit length)
Let's calculate the linear mass density (μ) of the wire first:
μ = m / L
Where:
m = mass of the wire
Given:
Length of the wire (L) = 38 cm = 0.38 m
Mass of the wire (m) = 6.0 g = 0.006 kg
Plugging in these values:
μ = 0.006 kg / 0.38 m
μ = 0.0158 kg/m
Now, we can calculate the fundamental frequency (f):
f = (1 / 2L) * √(T / μ)
f = (1 / 2 * 0.38 m) * √(145 N / 0.0158 kg/m)
Calculating further:
f = 1.32 Hz (approximately)
Therefore, the fundamental frequency of this wire is approximately 1.32 Hz.