Chapter 14, Problem 74A

To determine

The points that can be touched on a string vibrating in four parts without disturbing its motion.

Answer to Problem 74A

As there is destructive interference of the string, the string does not vibrate at the node points. The vibration or the movement of the string will not get disturbed if we touch it at the nodes. In the present case the string is vibrating in four parts so there will be three nodes.

Explanation of Solution

Introduction:

String vibration will produce standing wave. The nodes are the points where the amplitude of the waves goes to minimum value.

Any vibrating string will create a standing wave with nodes. These nodes have minimum amplitude. Touching these nodes will not disturb the pattern of the movement of the string and the vibrations it is producing. Any wave with $n$ number of vibrations will have $(n-1)$ number of nodes. The string is vibrating at four points and hence the number of nodes will be three.

Conclusion:

Hence, the numbers of nodes where the string can be touched without disturbing the vibration of string are three as the string is vibrating at four points.