Examining Beat Frequencies

Name:

Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10^-19 = 1.6E-19.

Procedure

1. Connect one signal generator to the oscilloscope in parallel with the speaker. Connect the frequency counter in parallel with the generator. Adjust the oscilloscope so that at most one complete sine wave appears on the screen. The number of (approximately 1 cm) time "divisions" on the screen between two successive peaks times the "time per division" setting on the scope gives the period of the wave. Compute the frequency (1 / period) from the scope, and verify this computation with the frequency counter meter. IF THE METER IS NOT WITHIN 10 % OF YOUR COMPUTED FREQUENCY, MEASURE THE FREQUENCY MORE CAREFULLY!

   Time / div = ms / div

   # of divisions =

   Period = s

   n_scope = Hz

   n_meter = Hz

2. Repeat the last step three more times for different frequencies. Note the relationship between the wave form and the frequency.

   Time / div = ms / div

   # of divisions =

   Period = s

   n_scope = Hz

   n_meter = Hz

   Time / div = ms / div

   # of divisions =

   Period = s

   n_scope = Hz

   n_meter = Hz

   Time / div = ms / div

   # of divisions =

   Period = s

   n_scope = Hz

   n_meter = Hz

3. Connect the other generator in parallel with the first. Adjust both frequencies to 1000 Hz. Adjust the oscilloscope until several waveforms are displayed on the screen. Slowly vary one above and below 1000 Hz and sketch qualitative changes in the resulting waveform as they occur. Describe the changes in terms of frequencies and phases:

4. Set the generators for the kHz range. Find and stabilize a beat waveform with a beat frequency around an order of magnitude less than the generator frequencies (this will necessitate the fine adjustment of both frequency and amplitude of the generators, the trigger level on the oscilloscope, and some patience). Record the frequencies of the generators and the beat frequency from the oscilloscope. Note the beat frequency as a range, corresponding to the visual error of measurement:

   Time / div = ms / div

   # of divisions_min = # of divisions_max =

   Period_min = s, Period_max = s

   n_{1, scope, min} = Hz, n_{1, scope, max} = Hz

   n_{1, meter 1} = Hz, n_{1, meter 2} = Hz

5. Repeat the last step with three other frequency differences, at least one of which is in the 10 kHz range:

   Time / div = ms / div

   # of divisions_min = # of divisions_max =

   Period_min = s, Period_max = s

   n_{2, scope, min} = Hz, n_{2, scope, max} = Hz

   n_{2, meter 1} = Hz, n_{2, meter 2} = Hz

   Time / div = ms / div

   # of divisions_min = # of divisions_max =

   Period_min = s, Period_max = s

   n_{3, scope, min} = Hz, n_{3, scope, max} = Hz

   n_{3, meter 1} = Hz, n_{3, meter 2} = Hz

   Time / div = ms / div

   # of divisions_min = # of divisions_max =

   Period_min = s, Period_max = s

   n_{4, scope, min} = Hz, n_{4, scope, max} = Hz

   n_{4, meter 1} = Hz, n_{4, meter 2} = Hz

Analysis

1. Compute the average of the range of beat frequencies recorded from the oscilloscope for each of the four beat patterns observed:

   n1, scope, avg = Hz				n3, scope, avg = Hz
   n2, scope, avg = Hz				n4, scope, avg = Hz

2. Calculate the beat frequencies from the meter frequencies (their difference):

   n1, beat = Hz				n3, beat = Hz
   n2, beat = Hz				n4, beat = Hz

3. Compute the absolute value of the difference between the computed (beat) and measured (scope) beat frequencies:

   n1, abs = Hz				n3, abs = Hz
   n2, abs = Hz				n4, abs = Hz

   Compute the relative error in this measurement:

   n_{i, rel} = n_{i, abs} * 100 % / n_{i, beat}

   n1, rel = %				n3, rel = %
   n2, rel = %				n4, rel = %

   Compare n_{i, abs} with the frequency range read from the scope. Is the error solely attributable to oscilloscope measurement?