SBU Intro Physics Labs, PHY 133 Standing Waves Lab

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Stony Brook University PHY 133 TABLE OF CONTENTS Introduction Equipment Background Procedure Analysis Questions References and Tools Introduction In this lab, we will study standing waves on both stretchy and rigid string. Hover over these! Back to Top Equipment 1 Elect ...[Show More]

Stony Brook University
PHY 133
TABLE OF CONTENTS

Introduction

Equipment

Background

Procedure

Analysis

Questions

References and Tools

Introduction

In this lab, we will study standing waves on both stretchy and rigid string. Hover over these!

Back to Top

Equipment

1 Electric Motor

1 Variable Power Supply

1 Photogate, LoggerPro file "StandingWaves"

2 Strings: 1 Yellow Stretchy, 1 White Non-Stretchy

1 Pulley

Various Masses

1 Meter Stick

1 Scale

Record data in this Google Sheets data table

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Background

Basics of Standing Waves

Suppose you have a long horizontal string. 1 Suppose the string is under tension and has a linear mass density (mass per unit

length) of (both of which are independent of your position along the string).

If the string is "free" (or you look far away from the endpoints), then you will find waves that "propagate" along the string with

some speed . 1 This speed can be calculated in terms of the parameters of the string: 2

We will not be looking at this case, but the velocity is a key parameter of the string regardless. We will instead be looking at

standing waves, which is what happens when we hold the string still at both ends. 2

A special class of solutions in this case are the harmonics. These are sine functions that oscillate with a frequency and a

wavelength . This means that your vertical 3 oscillations make the string have a vertical position of:

The velocity is then related to the frequency and the wavelength according to the simple formula:

The zeroes of the above function, (for any integer), are known as the nodes of the wave. The "flat" points

(maxima/minima), , are known as the antinodes.

Note that the endpoints of the string, and , are both always nodes (since we hold those points still), meaning that

there is some integer for which . (We use to refer to the specific integer that gives the zero corresponding to

.)

FT

μ

v

v = √ FμT (1)

v

f

λ y(x, t)

y(x, t) = sin( 2πλx ) [A sin(2πft) + B cos(2πft)] (2)

v = fλ (3)

x = m λ

2 m

x = λ

m+ 1

2

2