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

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.

Longitudinal Standing Waves In Closed 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 Harmonic First 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 Harmonic Second Overtone

Longitudinal Standing Waves In Open 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 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 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 Harmonic Second Overtone

 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.

Consider a standing wave in a closed organ pipe. First Harmonic Fundamental Third Harmonic First Overtone Fifth Harmonic Second Overtone same frequency Keeping the same frequency but making the pipe three times longer same frequency 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. For this length pipe the fundamental would look like this. This fundamental wavelength is three times longer and thus has a frequency of 1/3 of this third harmonic.

Consider a standing wave in an open organ pipe. First Harmonic Fundamental Second Harmonic First Overtone Third Harmonic Second Overtone same frequency Keeping the same frequency but making the pipe two times longer same frequency 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.

v  In this experiment you will need to calculate the wavelength of a wave based on knowing the speed and frequency.  Remember that = f or v = f