A phone cord is 4.75 m long. The cord has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.900 s. What is the tension in the cord?
To find the tension in the cord, we can use the formula for the speed of a wave on a string:
v = √(T/μ)
where:
v = wave speed
T = tension in the cord
μ = linear mass density of the cord
The linear mass density (μ) is defined as the mass per unit length of the string. It is calculated by dividing the mass of the cord by its length:
μ = m / L
where:
m = mass of the cord
L = length of the cord
In this case, the length of the cord is given as 4.75 m and the mass is given as 0.200 kg, so we can substitute these values into the equation to find μ.
μ = 0.200 kg / 4.75 m = 0.0421 kg/m
Now we can use the equation for wave speed to find the speed of the wave:
v = √(T/μ)
The wave travels four trips down and back along the cord in 0.900 s, so we can calculate the wave speed as:
v = 4 * (2L) / t
where:
L = length of the cord
t = time for four trips
Now we can equate these two formulas for wave speed and solve for the tension T:
4 * (2L) / t = √(T/μ)
To find T, we square both sides of the equation:
(4 * (2L) / t)^2 = T / μ
And solving for T:
T = μ * (4 * (2L) / t)^2
Now we substitute the known values:
T = 0.0421 kg/m * (4 * (2 * 4.75 m) / 0.900 s)^2
Calculating this expression will give us the tension in the cord.