# Waves Motion in a Slinky

## Objective

To demonstrate that wave velocity depend on tension and mass density.

## Introduction

The velocity of a wave on string is given by \(v=\sqrt{T/\mu}\), where \(T\) is the tension in the wire and \(\mu\) is its mass per unit length. A slinky, when stretched, offers a nice medium for demonstration of wave aspects. The number of turns per unit length acts for linear mass density and tension is the force by which each turn is pulled by its neighbour.

## Apparatus

A slinky

## Procedure

Put the slinky on the floor and ask two students to hold the two ends. Stretch the slinky to extend it to about four times of its natural length. Now pull one coil at one end and release. You will visibly see the wave pulse going along the slinky to the other end. The pulse will get reflected back and forth and finally die away. Have a mental estimate of the speed with which the wave moves on the slinky.

Now stretch the slinky more to increase its length say by a fraction of two. Again pull one coil at one end and release. You will again see wave pulse on the slinky but this time the speed will be much larger.

## Discussion

Why did the speed increase? By stretching it further you have increased the tension and decreased the number of turns per unit length. Thus effective \(T\) increased and effective \(\mu\) decreased. Both these results in increase in wave speed according to the equation \(v=\sqrt{T/\mu}\).