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Chapter 14: Problem 6

A heavy cable is hanging vertically, its bottom end free. How will the speed of transverse waves near the top and bottom of the cable compare? Why?

Short Answer

Expert verified
The speed of transverse waves will be higher near the bottom of the cable compared to the top, due to the increased tension at the bottom caused by the cumulative effect of gravity.

Step by step solution

01

Understand the structure of the cable

As the cable is hanging vertically, the weight it carries is unevenly distributed. It's heavier at the bottom 'coz of the cumulative effect of gravity pulling down the cable's material, and weighs less towards the top.
02

Determine the effect on the wave speed

The speed of a wave is directly related to the medium it travels through. In this case, the medium is the cable with uneven weight distribution. Since the wave speed depends mostly on the medium's tension, the cable's part bearing more weight (the bottom part here) will have a higher tension. Thus the wave speed will be faster near the bottom.
03

Compare the speeds

The transverse wave speed at the bottom of the cable will be faster than nearer the top due to differing tensions.

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