Standing Waves

Introduction

This experiment is designed to study a simple mechanical system: a string fixed at both ends. This system has a set of natural frequencies, at which standing waves are formed. If the string is driven by an external source with some frequency, the string will experience the strongest vibrations if this frequency is equal to one of the natural frequencies of the system.

Equipment

· Pasco WA-9611/9613 Sonometer, which includes:

o Sonometer base with tensioning lever

o Two bridges

o 10 wires (guitar strings) of five different diameters

o Instruction manual

o Weight hanger and weights

· Audio generator

· Amplifier

· Driver

· Detector

· Oscilloscope or frequency meter

Procedure

1. Set up the sonometer according to the instruction manual.

2. To create and detect a standing wave, you need to supply a signal from the audio generator (50 W output) which is amplified by the Krohn-Hite amplifier, to a driver placed under the string. The vibrations created by the driver can be picked up by a detector coil connected to the oscilloscope or frequency meter.

3. Study the dependence of the frequencies for at least the first 3 or 4 modes on the length of the wire, tension and linear density of the wire.

® Does the location of the nodes and antinodes depend on the tension and linear density?

® Does it matter if you have the driver near a node or an antinode?

® Determine a mathematical relationship between the higher order frequencies and the lowest (fundamental) natural frequency.

® Determine the dependence of the velocity of propagation v on tension T and linear density m . Find the exact mathematical form of this dependence assuming that , that is, find k, n and p.

Note: the response of this system has been found to be strongly dependent on the drive frequency. What about dependence on the drive amplitude?