A phone cord is 3.55 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 0.775 s. What is the tension in the cord?
To find the tension in the cord, we can use the formula for the velocity of a wave on a string:
v = √(T/μ),
where v is the velocity of the wave, T is the tension in the cord, and μ is the linear mass density of the cord.
First, let's calculate the velocity of the wave using the given information. We know that the wave travels a distance of 2 * 3.55 m in 0.775 s (four trips down and back). So, the velocity of the wave can be calculated as:
v = (2 * 3.55 m) / (0.775 s) = 9.16 m/s.
Now, we need to find the linear mass density of the cord, μ. The linear mass density is the mass per unit length of the cord and can be calculated as:
μ = m / L,
where m is the mass of the cord and L is the length of the cord.
Plugging in the given values, we have:
μ = 0.200 kg / 3.55 m = 0.0563 kg/m.
Now, using the equation v = √(T/μ), we can rearrange it to solve for T:
T = v^2 * μ,
T = (9.16 m/s)^2 * 0.0563 kg/m = 4.18 N.
Therefore, the tension in the cord is approximately 4.18 N.