Laboratory #6: Equivalence of Standing Waves and Traveling Waves

Objective:

We measured the frequency of a mode in a cavity and calculated the wavelength for the corresponding STANDING waves. From this we calculated a speed. This number is useful, but how do we really know that it corresponds to the velocity of something? Also, we do not yet know that standing waves and traveling waves are related. In this laboratory we will measure the speed of sound for TRAVELING waves. We will also demonstrate that two traveling waves can form a standing wave. Remember:

frequency× wavelength = velocity.

Equipment:
  1. Computer and PASCO software.
  2. Two computer speakers
  3. Amplifier in AMP setting.
  4. Plastic support bracket.
  5. Microphone on optical rail with ruler.

Diagram:

 

 

Instructions:

PART A:

  1. Start up PASCO software and open the file Lab6.sws.

  2. Start function generator and use a sine wave.

  3. Place the speaker and microphone as shown. Only turn on Speaker A.

  4. On the oscilloscope, the green trace is the output of the function generator and the red trace is from the microphone. As you move the microphone towards and away from the speaker, the red trace will move past the green. Movement of one full wavelength will shift the traces by one cycle. From this, you can determine the wavelength of the sound wave. Note, if possible, shift by many wavelengths and divide by the number you shifted past.

  5. Start at 5000 Hz. Then divide the frequency by two each time until you cannot measure a full wavelength. Then go back and fill in frequencies until you have at least ten measurements.

 

PART B:

  1. Turn on Speaker B in addition to Speaker A and set the frequency to about 3500 Hz.

  2. Now, as you move the microphone between the speaker the amplitude measured by the microphone will go up and down. These are the antinodes and nodes. Because of various imperfections, the amplitude at the nodes will not be perfectly zero. Just look for minima and maxima.

  3. Record the positions of several antinodes and nodes.

 

DATA:

Part A:

Frequency (Hz)

Wavelength (m)

Velocity (m/sec)
     
     
     
     
     
     
     
     
     
     
     

 

 

Part B:

Node or antinode?

Position (cm)

Distance between node and antinode
     
     
     
     
     
     
     
     
     
     
     

 

Questions:

  1. Average all of your results for the speed of sound and compare to the temperature corrected value:

Speed of sound = (331.3 + 0.6T) m/sec

where T is the temperature in ° C

 

 

 

 

  1. Were your results more accurate for the shorter wavelengths or the longer wavelengths? Why is this?

    2.  

     

     

     

     

  2. Find the average distance between nodes and antinodes in Part B. How does this compare to the value you expect for a standing wave using the frequency you set?