Beat Frequency Homework

 

Instructions:

 

1.  Tape two sheets of notebook paper together (end-to-end).  Overlap the papers by 1 inch.  This will give you a total length of 21 inches (remember that paper is 81/2” x 11”).

 

2.  Draw a line from one end of the paper to the other.  Draw it in the center of the paper.  Your line will be 21 inches long.

 

3.  Put a tick mark every 1 cm the entire length of the line in ONE COLOR.  Label these tick marks 0, 1, 2, 3, 4, 5, 6…etc.  You should have about 52 tick marks.

 

4.  Put a tick mark every 0.9 cm the entire length of the line in A DIFFERENT COLOR.  Label these tick marks 0, 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3….etc (notice that each tick mark is 0.9 more than the previous one)

 

5.  At the points at which these tick marks overlap, circle these points.

 

6.  Draw a wave through these points.  Use ONE COLOR for the 1 cm spaced points and a DIFFERENT COLOR for the 0.9 cm spaced points.  These points are the NODES of the wave.  Therefore, the anti-node of the wave (aka the “wave crest”) should be exactly half-way between each point.  The node of each wave should be on each point.

 

See the diagram below.  It should help you with steps 2-6.  Notice how I color coordinated the instructions with the diagram (how cool is that?!)

 

 

Questions:

 

1.  Fact:  The tick marks represent the nodes of the wave.

     Question:  How many tick marks makes 1 wavelength?  ___________

 

2.  Fact:  Notice that the tick marks first overlap at the 0 mark.  The next time they overlap is at the 9 cm mark.

     Question:  How many wavelengths are there between 0 and 9 of the wave generated on the 1 cm spaced tick marks?  _________

 

3.  How many wavelengths are there between 0 and 9 of the wave generated on the 0.9 cm spaced tick marks?  _________

 

4.  Fact:  Let’s assume that each tick mark is a number of seconds. 

     Question:  What is the frequency of the waves on the 1 sec spaced tick marks?  Remember that frequency = # of wavelengths/time  ______________ Round to 6 numbers after the decimal point – this is important!

 

5.  What is the frequency of the waves on the 0.9 sec spaced tick marks?  Remember that frequency = # of wavelengths/time  ______________  Round to 6 numbers after the decimal point – this is important!

 

6.  What is the difference in the frequency of the two waves?  (by difference, I mean subtraction!)   ______________  Round to 6 numbers after the decimal point – this is important!

 

7. Convert this difference in frequency into period (remember that T = period = 1/f)

__________________ Round to 6 numbers after the decimal point – this is important!

 

8.  Look at your drawing.  What does the period of the differences between the frequencies tell you about the frequency of constructive or destructive interference of this wave pattern?  ______________

 

9.  How many seconds (or centimeters, since cm = seconds in this example) elapse between one constructive interference and the next constructive interference?  ___________

 

10.  How many seconds (or centimeters, since cm = seconds in this example) elapse between one constructive interference and the next destructive interference?  ___________

 

Okay, now that you have answered these questions, lets try a real life example with a tuning fork.

 

Scenario 1:  Assume you have two tuning forks.  One has a frequency of 630 Hz.  The other has a frequency of 632 Hz.

 

1.  What is the difference in their frequency?  _________Hz. 

Fact:  This is called the BEAT FREQUENCY!

 

2.  How many loud/quiet (constructive/destructive) interference spots will you hear each second? _______

Fact:  This is called the BEAT FREQUENCY!

 

3.  How many seconds will elapse between EACH loud/quiet spot?  __________

Fact:  This is called the BEAT PERIOD!  Now you are looking at the number of seconds per loud/quiet spot.  Whereas, with the BEAT FREQUENCY, you were looking at the number of loud/quiet spots per ONE second.

 

Scenario 2:  two tuning forks with the frequencies 630 Hz and 740 Hz

 

1.  What is the difference in their frequency?  _________Hz. 

Fact:  This is called the BEAT FREQUENCY!

 

2.  How many loud/quiet (constructive/destructive) interference spots will you hear each second? _______

Fact:  This is called the BEAT FREQUENCY!

 

3.  Why will you not be able to hear these beats, but with the ones made by the previous set of tuning forks you could hear beats (loud quiet spots)

 

4.  How many seconds will elapse between EACH loud/quiet spot?  __________

Fact:  This is called the BEAT PERIOD!  Now you are looking at the number of seconds per loud/quiet spot.  Whereas, with the BEAT FREQUENCY, you were looking at the number of loud/quiet spots per ONE second.

 

5.  True or False:  In order for beats to be heard by the human ear, the two frequencies in question must be somewhat close to each other (not exactly the same, but close – like 1-3 Hz off from each other).