Answer to Question #103007 in Mechanics | Relativity for Nyx

Question

A phone cord is 6.75 m long. The cord has
a mass of 0.247 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 0.748 s.
What is the tension in the cord?
Answer in units of N.

Answer 1

The expression for mass per unit length of cord is

$$\frac{m}{l}$$

The pulse makes four trips down and back along the cord. So the pulse covered the 8 times of length of cord. The expression for velocity of pulse is

$$v=\frac{8l}{t}$$

The expression for velocity of pulse in terms of tension and mass per unit length is

$$v=\frac{8l}{t}=\sqrt{\frac{T}{\frac{m}{l}}}$$

$$\frac{8( 6.75)}{0.748}=\sqrt{\frac{T}{\frac{0.247}{ 6.75}}}$$

$$T=191\ N$$