Respuesta :
Answer:
(a). The value of A, k and ω is [tex]2\times10^{-4}\ m[/tex], 16.02 rad/m and 3141.59 rad/s.
(b). The tension in the wire is 157.5 N.
Explanation:
Given that,
Amplitude = 0.200 mm
Frequency = 500 Hz
Speed = 196 m/s
Mass per unit length = 4.10 g/m
Suppose we need to calculate the parameters A, k, and ω.
The equation given by
[tex]y=A\sin(kx-\omega t)[/tex]
(a). We need to calculate the amplitude
Using formula of amplitude
[tex]A=0.200\times10^{-3}\ m[/tex]
[tex]A=2\times10^{-4}\ m[/tex]
We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega=2\pi f[/tex]
[tex]\omega=2\times\pi\times500[/tex]
[tex]\omega=3141.59\ rad/sec[/tex]
We need to calculate the angular wave number
Using formula of angular wave number
[tex]k=\dfrac{\omega}{v}[/tex]
Put the value into the formula
[tex]k=\dfrac{3141.59}{196}[/tex]
[tex]k=16.02\ rad/min[/tex]
(b). We need to calculate the tension in the wire
Using formula of tension in the wire
[tex]T=v^2\times\mu[/tex]
Put the value into the formula
[tex]T=196^2\times4.10\times10^{-3}[/tex]
[tex]T=157.5\ N[/tex]
Hence, (a). The value of A, k and ω is [tex]2\times10^{-4}\ m[/tex], 16.02 rad/m and 3141.59 rad/s.
(b). The tension in the wire is 157.5 N.
Answer:
(a) y = (0.2 x 10^-3 m)Sin (16 x - 3140 t)
(b) 157.5 N
Explanation:
Amplitude, A = 0.2 mm
Frequency, f = 500 Hz
velocity,v = 196 m/s
(a) The standard equation of a wave is
y = A Sin (kx - ωt)
Where, k = 2π/λ
where, λ is the wavelength
λ = v / f = 196 / 500 = 0.392 m
So, k = 2 x 3.14 / 0.392 = 16
ω = 2 x π x f = 2 x 3.14 x 500 = 3140 rad/s
So, the equation is
y = (0.2 x 10^-3 m)Sin (16 x - 3140 t)
(b) mass per unit length, m = 4.10 g/m = 4.10 x 10^-3 kg/m
The velocity
[tex]v=\sqrt{\frac{T}{m}}[/tex]
T = v² x m
T = 196 x 196 x 4.10 x 10^-3 = 157.5 N
Thus, the tension in the wire is 157.5 N.
