The Organ PipeThe Organ Pipe

During the last two labs you explored During the last two labs you explored the superposition of waves and the superposition of waves and standing waves on a string.standing waves on a string.

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

Today you continue to study Today you continue to study interference by looking at standing interference by looking at standing waves in organ pipes.waves in organ pipes.

Standing WavesStanding Waves When 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 in open and closed organ pipes.

Longitudinal Standing WavesLongitudinal Standing Waves

In In

Closed Organ PipesClosed Organ Pipes

When sound waves pass down a closed pipe and reflect from the other end, you have a situation in which two waves are traveling in opposite directions and occupying the same region of space at the same time.

Under the proper conditions a longitudinal standing wave can be established with an antinode at the open end and a node at the closed end.

Again the lowest frequency standing wave that can be established is called the first harmonic.

Its standing wave pattern looks like this. (Plotted as displacement of air molecules versus position in the tube.)

This frequency is also called the fundamental.

First Harmonic

Fundamental

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, 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.

Third HarmonicFirst Overtone

Since this frequency is five times the first harmonic, it is referred to as the fifth harmonic.

Since this frequency is the next higher frequency occurring in the pipe, 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.

Fifth HarmonicSecond Overtone

Longitudinal Standing WavesLongitudinal Standing Waves

In In

Open Organ PipesOpen Organ Pipes

When sound waves pass down an open pipe and reflect from the other end, you again have a situation in which two waves are traveling in opposite directions and occupying the same region of space at the same time.

Under the proper conditions a standing wave can be established with an antinode at each end.

Again the lowest frequency standing wave that can be established is called the first harmonic.

Its standing wave pattern looks like this. (Plotted as displacement of air molecules versus position in the tube.)

This frequency is also called the fundamental.

First Harmonic

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, 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 occurring in the pipe, 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 In the experiment today you will determine the lengths of pipe determine the lengths of pipe necessary to create different necessary to create different standing wave patterns.standing wave patterns.

You will also discover that a You will also discover that a particular frequency will be a particular frequency will be a first harmonic for one length of first harmonic for one length of pipe and yet a different harmonic pipe and yet a different harmonic for a different length pipe.for a different length pipe.

The next two slides will illustrate The next two slides will illustrate this.this.

Consider a standing wave in a closed organ pipe.Consider a standing wave in a closed organ pipe.

First Harmonic

Fundamental

Third Harmonic

First Overtone

Fifth Harmonic

Second Overtone

Keeping the same frequencysame frequency but making the pipe three times longer

Keeping the same frequencysame frequency but making the pipe five timesthe original length

This shows that a particular frequency can be a first harmonic for one pipe, a third harmonic for a longer pipe and a fifth harmonic for an even longer pipe.

For this length pipethe fundamental would look like this.

This fundamental wavelengthis three times longer and thushas a frequency of 1/3 of thisthird harmonic.

Consider a standing wave in an open organ pipe.Consider a standing wave in an open organ pipe.

First Harmonic

Fundamental

Second Harmonic

First Overtone

Third Harmonic

Second Overtone

Keeping the same frequencysame frequency but making the pipe two times longer

Keeping the same frequencysame frequency but making the pipe three timesthe original length

This shows that a particular frequency can be a first harmonic for one pipe, a second harmonic for a longer pipe and a third harmonic for an even longer pipe.

v

In this experiment you will need In this experiment you will need to calculate the wavelength of a to calculate the wavelength of a wave based on knowing the wave based on knowing the speed and frequency.speed and frequency.

Remember thatRemember that

= for

v= f