Resonance & Speed of Sound Lab            Name: ______________________

Conceptual Physics                                                       Period: ___

 

Resonance occurs whenever something is forced to vibrate (by an outside object) at its own natural frequency.  When this happens, the amplitude of the vibration increases dramatically.  If the vibration is producing sound, we hear the increase in amplitude as an increase the volume of the sound.

     The most common place to see resonance is in tubes.  Most musical instruments are just tubes with 2 open ends (open-open) or one open and one closed end (open-closed).  The air in the instrument is forced to vibrate by the oscillation at the end (the reed, or the player's lips, etc.).  If one of the frequencies of the vibration matches the natural frequency of the air in the tube, the air resonates and vibrates with a large amplitude, making a loud sound.  (Any of the vibrations that don't match the natural frequency make the air vibrate, but with a small amplitude so you can't hear them.) 

     The way that you change the tone (or pitch) that the instrument plays is to change the length of the tube, which changes the air's natural frequency.  In this lab we will play with different tubes and change their lengths until their natural frequency matches the frequency of the tuning fork that is forcing them to vibrate.

Materials:  10 stations with tuning fork, rubber mallet and resonance tube (two pieces of PVC pipe or one piece of PVC pipe in large graduated cylinders)

Procedure:


1.  Measure the temperature in the classroom by checking the thermometer in the beaker full of water on the front table:

Temperature:               


2. When you come to a new station, identify whether it is an open-open tube or an open-closed tube and follow the correct instructions for that type of tube.

Instructions for an open-open tube: there are 3 open-open tubes you will test each once and record the data in the table below.

 

Open-Open Tube Data

Frequency of Tuning Fork

Measured Length of Tube at Max Amplitude

Calculated Wavelength for that note

Calculated speed of sound

Percent Error from the actual speed of sound at room temperature

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1st  Find the frequency printed on the side of the tuning fork at the station and record it in your table.

2nd  Strike the tuning fork with the mallet.  !!FAILURE TO USE THE MALLET MAY DAMAGE THE TUNING FORK!! YOU BREAK IT, YOU BUY IT.

3rd  Hold the vibrating tuning fork at an open end of the resonance tube so that the tuning fork's vibrations are directed along the length of the tube.  Prongs lined up along length of tube, like in the diagram.

4th Adjust the tube's length until you hear the volume of the sound increase to its highest amplitude.  THIS IS RESONANCE!  Do not be fooled by small peaks in volume, wait until you hear a very clear increase in volume!

5th Measure the length of the column for which you get resonance.  For an open-open tube, that is the length from one open end to the other (the combined length of both tubes).  Be sure to convert your measurement into meters and record the length in your Open-Open Tube data table.

6th Take data for all of the different stations you are going to do and then wait to do the data analysis.

 

Instructions for an Open-Closed Tube There are three open closed tubes record the data from in one in the table below.

 

Open-Closed Tube Data Table

Frequency of Tuning Fork

Measured Length of Tube at Max Amplitude

Calculated Wavelength for that note

Calculated speed of sound

Percent Error from the actual speed of sound at room temperature

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1st  Find the frequency printed on the side of the tuning fork at the station and record it in your table.

2nd  Strike the tuning fork with the mallet.  !! DO NOT USE ANY OBJECT OTHER THAN THE MALLET!! FAILURE TO FOLLOW THIS MAY DAMAGE THE TUNING FORK!

3rd  Hold the vibrating tuning fork at an open end of the resonance tube so that the tuning fork's vibrations are directed along the length of the tube.  Prongs lined up along length of tube, like in the diagram.

4th  Adjust the tube's length until you hear the volume of the sound increase to its highest level.  THIS IS RESONANCE!  Do not be fooled by small resonances or peaks in volume, wait until you hear a very clear increase in volume!

5th  Measure the length of the column for which you get resonance. 

For an open-closed tube, measure the length from the open end to the surface of the water (this represents the closed end).  Be sure to convert your measurement into meters and record the length in your Open-Closed Tube data table

6th  Take data for all of the different stations you are going to do and then wait to do the data analysis.

 

 

Graph

Create a Graph that compares length of the two types of tubes when resonating to the same note.

 

 

 

Questions

Answer the following questions by looking at your results in your data tables and your knowledge of resonance. 

1. What is the relationship between the length of an open-open tube and the frequency of the sound that resonates in it?

 

2.  What is the relationship between the length of an open-closed tube and the frequency of the sound that resonates in it?

 

3.  If you want to have your didgeridoo, flute, trombone, etc. play a lower note, what do you have to do to the tube? Think about how a musician changes the note they are playing. If they want the note to be low in frequency what to they do compared to if they want to play a high frequency note.

 

 

 

4.  Compare an open-open tube and an open-closed tube that resonate at close to the same frequency.  How do the lengths of the tubes compare? Give the exact about one will be longer than the other.

 

 

5.  Compare an open-open tube and an open-closed tube that are approximately the same length.  How do the frequencies that resonate in each tube compare? Again give the exact about greater one frequency will be than the other.

 

 

 

6.  If you were building a pipe organ in a small church and wanted to get the lowest sound possible out of your pipes, what type of tube would you use:  open-open or open-closed?

 

 

 

 

Resonance & Speed of Sound Lab Analysis

     When any object vibrates at its natural frequency or is made to resonate, that means that there is a standing wave inside the object.  In a tube full of air, that wave will be a standing sound wave.  Because standing waves have to have either nodes or antinodes at the edges of the object, the length of a resonating tube can tell us the wavelength of the sound waves.  The relationship between wavelength and length of the resonating tube depends on which type of tube it is:  open-open or open-closed.

Open - Open                                                        Open - Closed

                                                     

   

 

 

 

If you know the wavelength of the sound wave then all you need to know                                     Wave Speed Equation

is the frequency of the sound wave and it is simple to calculate the speed of the sound wave using the wave-speed equation.  We will use our knowledge of resonance and standing waves to find the speed of sound several times and see how accurately we can get.  With a little bit of effort, you can get very accurate values for the speed of sound in air so really try to make all your measurements as accurately as you can.

 

We will compare our data to the expected value of the speed of sound.                                   Expected Speed of Sound

Previous research has given us a formula to calculate the expected

speed of sound:  s = 332 m/s + 0.6 m/s (T), where s is the speed                                                   s =             

of sound and T is the temperature in degrees Celsius, which you measured

last class.

 

Procedure - Day 2

1. For each tube and tuning fork that you measured, use the appropriate tube equation to find the wavelength based on the measured length of the resonating tube.  Use the open-open tube equation for open-open tubes and the open-closed tube equation for open-closed tubes. Record these calculations in the second half of the data tables above.

2.  Once you have the frequency and wavelength, use the wave speed equation (as seen on the first page of this lab) to calculate the speed of the sound wave based on its wavelength and frequency.

3. After you have calculated the speed of sound for all of your trials, average your results for each type of tube

4. Calculate the percent “error” for the average speed on each type of tube, using the following formula:

Percent “Error” = x 100%

 

Questions

Answer the following questions using the results in your data table and the equations for both types of tubes.

7.  Which type of tube gave you the lowest percent error, open-open or open-closed?  Why do you think there was a difference?

 

 

8. How long would a trombone (what type of tube is a trombone?) have to be to produce a 3.4 m long sound wave?

 

 

9.  How long would the sound-making portion of a flute be when you make a sound wave with a frequency of 900 waves/sec?  (Assume speed of sound = 343 m/s)

 

 

10.  What frequency sound wave will you get from a jug that is .4 m (40 cm) tall?(Assume speed of sound = 343 m/s)