Chapter 11, Problem 18Q

To determine

If a string is vibrating as a standing wave in three loops, determine if there are any places you could touch it with a knife blade without disturbing the motion.

Answer to Problem 18Q

Solution:

Touching it at the nodes will not disturb the motion.

Explanation of Solution

In a standing wave there are positions known as nodal points or nodes where there is no vibration. A node is a point which does not move while the transverse waves pass, where all waves cancel or pass through without moving any particles and can be touched it with a knife blade without disturbing the motion.

As the string is vibrating in three loops, it should have four nodes (two at the ends, and two in between).

Conclusion:

Nodes are points of no displacement and they are characteristic of every standing wave pattern, which can be touched without interrupt the motion.