the vibrating string. during the last lab you explored the superposition of waves. when two waves...

The Vibrating The Vibrating StringString

During the last lab you explored the During the last lab you explored the superposition of waves.superposition of waves.

When two waves or more occupy the same When two waves or more occupy the same region of a medium at the same time, they region of a medium at the same time, they will interfere with each other.will interfere with each other.

In the last lab you learned about constructive In the last lab you learned about constructive interference, destructive interference, and interference, destructive interference, and partially constructive interference. partially constructive interference.

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

Standing WavesStanding WavesWhen two sets of waves of equal

amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern 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.

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

nodes or successive antinotes.

Parameters of a Standing WaveParameters of a Standing Wave

When you pluck a stringed musical instrument, the string vibration is composed of several different standing waves.

The lowest frequency carried by the string is called the first harmonic.

Its standing wave pattern looks like this.

First Harmonic

This frequency is also called the fundamental.

Fundamental

Since this frequency is twice the first harmonic, it is referred to as the second harmonic.

Since this frequency is the next higher frequency appearing on the string, it is called the first overtone.(It is the first tone above the fundamental.)

The next higher frequency standing wave pattern looks like the following.

Second HarmonicFirst Overtone

Since this frequency is three times the first harmonic, it is referred to as the third harmonic.

Since this frequency is the next higher frequency appearing on the string, it is called the second overtone.(It is the second tone above the fundamental.)

The next higher frequency standing wave pattern looks like the following.

Third HarmonicSecond Overtone

In the experiment today you will adjust In the experiment today you will adjust the tension in a vibrating string so that the tension in a vibrating string so that you create different standing wave you create different standing wave patterns.patterns.

(Adjusting the tension in the string (Adjusting the tension in the string changes the speed of the wave.) changes the speed of the wave.)

Important Note:Important Note:

The frequency of vibration on your The frequency of vibration on your string will remain constant.string will remain constant.

By changing the wave speed you will be By changing the wave speed you will be changing the wavelength and therefore changing the wavelength and therefore the harmonic number of the standing the harmonic number of the standing wave.wave.

First Harmonic

Fundamental

To show this let’s put a first harmonic on the To show this let’s put a first harmonic on the string.string.

Second Harmonic

First Overtone

Next let’s loosen the string which will Next let’s loosen the string which will slow the wave down yielding a shorter slow the wave down yielding a shorter wavelength.wavelength.

Third Harmonic

Second Overtone

Loosening the string some more results in Loosening the string some more results in an even shorter wavelength.an even shorter wavelength.

Thus your Thus your frequencyfrequency of vibration will be a of vibration will be a first harmonic for a high tension in the first harmonic for a high tension in the string and different harmonics for lesser string and different harmonics for lesser tensions.tensions.

Note that a more accurate method of Note that a more accurate method of obtaining the frequency of a standing obtaining the frequency of a standing wave on a string could be wave on a string could be accomplished by using a strobe light accomplished by using a strobe light to make the wave appear to be to make the wave appear to be “standing still.” “standing still.”

All you would have to do is read the All you would have to do is read the frequency from the variable frequency from the variable frequency strobe light.frequency strobe light.

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 an overview of the experimental apparatus

By varying the mass on the mass By varying the mass on the mass hanger one can create standing waves hanger one can create standing waves with differing numbers of segments.with differing numbers of segments.