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The Organ Pipe. During the last two labs you explored the superposition of waves and standing waves on a string. Just as a reminder, when two waves or more occupy the same region of a medium at the same time, they will interfere with each other.

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Presentation Transcript
slide2
During the last two labs you explored the superposition of waves and standing waves on a string.
  • Just as a reminder, when two waves or more occupy the same region of a medium at the same time, they will interfere with each other.
  • Today you continue to study interference by looking at standing waves in organ pipes.
standing waves
Standing 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.
slide4
Longitudinal Standing Waves

In

Closed Organ Pipes

slide5
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.
slide6
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.)

First Harmonic

Fundamental

  • This frequency is also called the fundamental.
slide7
The next higher frequency standing wave pattern looks like the following.

Third Harmonic

First 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, it is called the first overtone.

(It is the first tone above the fundamental.)

slide8
The next higher frequency standing wave pattern looks like the following.

Fifth Harmonic

Second 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.)

slide9
Longitudinal Standing Waves

In

Open Organ Pipes

slide10
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.
slide11
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.)

First Harmonic

Fundamental

  • This frequency is also called the fundamental.
slide12
The next higher frequency standing wave pattern looks like the following.

Second Harmonic

First Overtone

  • 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.)

slide13
The next higher frequency standing wave pattern looks like the following.

Third Harmonic

Second 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.)

slide14
In the experiment today you will determine the lengths of pipe necessary to create different standing wave patterns.
  • You will also discover that a particular frequency will be a first harmonic for one length of pipe and yet a different harmonic for a different length pipe.
  • The next two slides will illustrate this.
slide15

Fifth Harmonic

First Harmonic

Third Harmonic

For this length pipe

the fundamental

would look like this.

Consider a standing wave in a closed organ pipe.

This fundamental wavelength

is three times longer and thus

has a frequency of 1/3 of this

third harmonic.

Fundamental

First Overtone

Second Overtone

Keeping the same frequency but making the pipe three times longer

Keeping the same frequency but making the pipe five times

the 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.

slide16

Third Harmonic

First Harmonic

Second Harmonic

Consider a standing wave in an open organ pipe.

Fundamental

First Overtone

Second Overtone

Keeping the same frequency but making the pipe two times longer

Keeping the same frequency but making the pipe three times

the 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.

slide17

v

l

=

f

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

v

f

=

l

or