The wave equation is missing and it is y(x,t) = (8.50 mm)cos(172 rad/m x − 4830 rad/s t)
Answer:
A) 0.0534 seconds
B) 0.67N
C) 41
D) (8.50 mm)cos(172 rad/m x + 4830 rad/s t)
Explanation:
we are given weight of string = 0.0125N
Thus, since weight = mg
Then, mass of string = 0.0125/9.8
Mass of string = 1.275 x 10⁻³ kg
Length of string; L= 1.5 m .
mass per unit length; μ = (1.275 x 10⁻³)/1.5
μ = 0.85 x 10⁻³ kg/m
We are given the wave equation: y(x,t) = (8.50 mm)cos(172 rad/m x − 4830 rad/s t)
Now if we compare it to the general equation of motion of standing wave on a string which is:
y(x,t) = Acos(Kx − ω t)
We can deduce that
angular velocity;ω = 4830 rad/s
Wave number;k = 172 rad/m
A) Velocity is given by the formula;
V = ω/k
Thus, V = 4830/172 m/s
V = 28.08 m /s
Thus time taken to go up the string = 1.5/28.08 = 0.0534 seconds
B) We know that in strings,
V² = F/μ
Where μ is mass per unit length and V is velocity.
Thus, F = V²*μ =28.08² x 0.85 x 10⁻³
F = 0.67N
C) Formula for wave length is given as; wave length;λ = 2π /k
λ = 2 x π/ 172
λ = 0.0365 m
Thus, number of wave lengths over whole length of string
= 1.5/0.0365 = 41
D) The equation for waves traveling down the string
= (8.50 mm)cos(172 rad/m x + 4830 rad/s t)
