Question

A long rope with mass m is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope, and the pulse travels up the rope. Does the speed of the wave pulse change as it moves up the rope, and if so, does it increase or decrease? Explain.

Short answer

The speed of the wave pulse will change and the velocity will increase.

Step-by-step solution

Concept of the speed of the wave.

The change in position of the moving object with respect to time is called speed.

 STEP 2: Relation between speed and density 

If a rope (having mass) is suspended then the tension of the rope increases with the height and the speed is directly proportional to thetension of the string,

The wave speed is,

$\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$

Here, v is the speed, T is the tension, and $\mu$is the mass.

Therefore, the velocity increases as the pulse goes up.