Question

What is the speed of a transverse wave in a rope of length2.00 mand mass60.0 gunder a tension of 500 N?

Short answer

The speed of a transverse wave is 129.1 m/s

Step-by-step solution

The given data

• The length of the rope,L=2.00 m.
• The tension in the rope, T=5.00 N
• The mass of the rope,m =60.0 g=0.0600 kg

Understanding the concept of linear density

The mass per unit length of the wire is known as the linear density of the wire.

By finding the linear mass density of the rope, we can find the speed of the wave.

The wave speed in terms of tension and linear density,

$v=\sqrt{\frac{t}{\mu }}$ …..(i)

The linear density of a body,

$\mu =\frac{m}{L}$ …..(ii)

Calculation of the speed of the transverse wave

The linear mass density $\mu$of the rope using equation (ii) and the given values can be given as:

$$\begin{gathered} \mathrm{\mu }=\frac{0.0600\mathrm{kg}}{2.00\mathrm{m}} \\ =0.0300\mathrm{kg}/\mathrm{m} \end{gathered}$$

Thus, the wave speed using equation (i) is given as:

$$\begin{gathered} \mathrm{v}=\sqrt{\frac{500\mathrm{N}}{0.0300\mathrm{kg}/\mathrm{m}}} \\ =129.1\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the value of the speed of the transverse wave is 129.1 m/s