What is the linear mass density of the rope (in kg/m)?

Question

Two children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 4.1 m long, its mass is 0.60 kg, and the force exerted on it by the children is 55 N.

(a)

What is the linear mass density of the rope (in kg/m)?

(b)

What is the speed of the waves on the rope (in m/s)?

Answer 1

The linear density, λ, is given by:

λ = M / L

Where:

1. M = mass of the string
2. L = length of the string

Therefore, the linear density is:

1. λ = M / L
2. λ = 0.60 kg. / 4.1 m.
3. λ ≈ 0.146341463 kg. / m.
4. λ ≈ 0.15 kg. / m.

The speed of the wave is given by the equation:

v = √ ( T / λ )

Where:

1. v = velocity of the wave
2. T = the tension on the wave
3. λ = the linear mass density of the wave

Plugging-in the numbers into the last equation:

1. v = √ ( T / λ )
2. v = √ ( 55 N. / 0.15 kg. · m^-1 )
3. v ≈ 19.38642136
4. v ≈ 19 m. / s.