the vibrating string

7/27/2019 The Vibrating String

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The Vibrating String


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During the last lab you explored the superposition

of waves. When two waves or more occupy the same region

of a medium at the same time, they will interferewith each other.

In the last lab you learned about constructiveinterference, destructive interference, andpartially constructive interference.

Today you will continue to study interference bylooking at standing waves on a string.


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Standing Waves

When two sets of waves of equalamplitude and wavelength pass through

each other in opposite directions, it is

possible to create an interferencepattern that looks like a wave that is

standing still.

It is a changing interference pattern.

Today you will create such patterns on a

vibrating string.


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There is no vibration at a node.There is maximum vibration at an antinode.lis twice the distance between successive

nodes or successive antinotes.

l

Parameters of a Standing Wave


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When you pluck a stringed musicalinstrument, the string vibration iscomposed of several different standing

waves. The lowest frequency carried by the

string is called the first harmonic.

Its standing wave pattern looks likethis.

First Harmonic

This frequency is also called the

fundamental.

Fundamental


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Since this frequency is twice the firstharmonic, it is referred to as the secondharmonic.

Since this frequency is the next higherfrequency appearing on the string, it iscalled the first overtone.

(It is the first tone above thefundamental.)

The next higher frequency standingwave pattern looks like the following.

Second HarmonicFirst Overtone


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Since this frequency is three times the firstharmonic, it is referred to as the thirdharmonic.

Since this frequency is the next higherfrequency appearing on the string, it is calledthe second overtone.

(It is the second tone above the fundamental.)

The next higher frequency standing wavepattern looks like the following.

Third HarmonicSecond Overtone


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In the experiment today you will adjustthe tension in a vibrating string so that you

create different standing wave patterns.(Adjusting the tension in the stringchanges the speed of the wave.)

Important Note:The frequency of vibration on your stringwill remain constant.

By changing the wave speed you will bechanging the wavelength and therefore theharmonic number of the standing wave.


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First Harmonic

Fundamental

To show this lets put a first harmonic on the string.


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Second Harmonic

First Overtone

Next lets loosen the string which will slowthe wave down yielding a shorter wavelength.


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Third Harmonic

Second Overtone

Loosening the string some more results in an

even shorter wavelength.


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Thus your frequency of vibration will be afirst harmonic for a high tension in thestring and different harmonics for lessertensions.


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Note that a more accurate method ofobtaining the frequency of a standingwave on a string could be accomplishedby using a strobe light to make the waveappear to be standing still.

All you would have to do is read the

frequency from the variable frequencystrobe light.


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The electric oscillator is located here.Masses are added here.When the apparatus is turned on and with the propermass on the hanger, standing waves can occur.This is considered to be one segment.

Points of no vibration are called nodes.Three are shown here. (Where are they?)The large vibration areas are called antinodes.

Node

Antinodes

Electric Oscillator

One Segment

Hanger and Masses

The lab assistant will now give you anoverview of the experimental apparatus


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By varying the mass on the mass hangerone can create standing waves withdiffering numbers of segments.

the vibrating string

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