Answer:
Step-by-step explanation:
(a) The wave equation for a transverse wave is given by y = a * sin(kx - ωt), where:
- y is the displacement of the wave
- a is the amplitude
- k is the wave number
- x is the position coordinate
- ω is the angular frequency
- t is time
Given:
Amplitude (a) = 0.200 mm = 0.0002 m
Frequency (f) = 570 Hz
Speed (v) = 196 m/s
Angular frequency (ω) is related to frequency by ω = 2πf.
So, ω = 2π * 570 rad/s = 3594π rad/s
The wave number (k) is related to the speed and angular frequency by k = ω/v.
k = (3594π rad/s) / (196 m/s) ≈ 18.283 rad/m
The parameters a, k, and ω are:
a = 0.0002 m
k ≈ 18.283 rad/m
ω ≈ 3594π rad/s
(b) The tension (T) in the wire is related to the wave speed (v) and the mass per unit length (μ) by the equation:
v² = T / μ
Given mass per unit length (μ) = 4.50 g/m = 0.0045 kg/m
Speed (v) = 196 m/s
T = μ * v² = 0.0045 kg/m * (196 m/s)² ≈ 176.904 N
So, the tension in the wire is approximately 176.904 Newtons.