Question

A mass of 18.4 kg hangs from a 16.0 m rope it takes 0.545 s for a wave to propagate along the rope (remember, waves travel with constant speed).

a. What is the mass of the rope?

What is the wave speed if:

b. The mass of the hanging mass is doubled.

c. The mass of the rope is doubled.

Hw #3 Due Tuesday Jan 22 A mass of 18.4 kg hangs from a 16.0 m rope lt takes a 0.545 s for a wave to propagate along the rope (remember, waves travel with constant speed). a. What is the mass of the rope? What is the wave speed if: b. The mass of the hanging mass is doubled c. The mass of the rope is doubled. ㄩ 17

Answer 1

Speed of wave produced in the string U = squareroot T/m_rope L_rope where T rightarrow Tension in string m_rope rightarrow mass of the string L_rope rightarrow length of string In our case, the weight of mass 18.4 kg acts as tension T = Mg Then U = squareroot m g L_rope/m_rope or m_rope = m g L_rope/U^2 (1) Given that: Hanged mass m = 18.4 kg, gravity g = 9.8 m/s^2 Length of the rope L_rope = 16.0 m, time interval of travelling Delta t = 0.545 s Speed of wave U = L/Delta t = 16.0 m/0.545 s = 29.36 m/s Pulling these values in eqn. (1), we get m_rope = 18.4 kg times 9.8 m/s^2 times 16.0 m/(29.36 m/s)_^2 = 3.34 kg \r\n Part b U = squareroot m g L_rope/m_rope U alpha squareroot m = > U_2/U_1 = squareroot m_2/m_1 Given that hanging mass is doubled m_2/m_1 = 2 U_2 = squareroot 2 U_1 = squareroot 2